In the past, a parade of bold-face names sallied to this resort city on Mexico's balmy Pacific coast. Frank Sinatra sang about it. The Kennedys honeymooned and the Nixons holidayed here. Howard Hughes ended his days here, Elvis Presley made a movie and John Wayne and Johnny ''Tarzan'' Weissmuller opened the fabled Hotel Los Flamingos, one of scores that now stand sentinel by Acapulco Bay's emerald waters.

But the party days of the '50s and '60s are furthest from the mind of the white-cassocked Father Martin Reyna, as he tells matter-of-factly of how, after Mass on a recent morning, he stumbled upon an unidentified victim of the turf wars being waged by Mexico's drug cartels.

First - a bleeding torso. It had been dumped next to a makeshift flower stall, on the steps that separate the church from a choked intersection in the heart of Colonia La Garita, Reyna's parish that perches high on the slopes above the glittering tourist strip that drives 70 per cent of Acapulco's economy. Next - the head and limbs. A few metres down the hill towards the downtown area, these body parts were scattered on the pavement at the foot of a post on which a public telephone hangs.

''It's hell on earth,'' the priest says.

This was no isolated incident. Weeks earlier, two decapitated bodies were dumped in the night on the narrow overpass that spans the intersection, so that morning churchgoers were obliged to step around them. About the same time, another dismembered corpse dropped close to Reyna's church had a crude, unsigned note fixed to the chest: ''This is our place - we are here.''

Mexico's $US38 billion drug trade continues to defy the combined might of the country's authorities, including the military, and their US backers. Marking the fifth anniversary of a relentless counter-narcotics campaign, a threat assessment released by the US National Drug Intelligence Centre in August cut through the fog of political rhetoric on both sides of the border, to trumpet failure. ''Heroin, marijuana, MDMA [ecstasy] and methamphetamine are readily available throughout the US - and their availability is increasing in some markets,'' it states.

Most of that heroin and marijuana is smuggled into the US from Mexico and, increasingly, is distributed domestically by offshoots of the Mexican cartels. Despite the crackdown in Mexico, the cartels have surged on the global heroin-production ladder, jumping from fifth in 2005 to second, behind only Afghanistan, in 2009, the threat assessment says.

The nearest the American document comes to being upbeat is on the cocaine trade - availability in the US was back to pre-2007 levels as a result of decreased Colombian production and the diversion of some shipments to Europe. The classic signs of reduced supplies - higher street prices (up 69 per cent on 2007) and reduced purity (down 30 per cent) - were reported. But while cocaine supplies were at less than the levels of 2006 east of the Mississippi, the reverse was the case west of the river.

The hourglass geography of the Americas - with North and South America as the bulges and Mexico as the pinch - graphically explains the drug trade. To the south, there is massive drug production and, as Mexican President Felipe Calderon bitterly complains, to the north, an insatiable appetite for drugs. Mexico is the conduit through which supply satisfies demand.

But more disturbing than the resilience and inventiveness of the cartels is the pervasive, bestial violence by which their militias carve out territory - for local sales, but also for smuggling routes to the US market.

Equally disturbing is the line - put up by officials in Mexico City and tourism operators here in Acapulco - that 45,000 to 60,000 drug-related murders across the country in just five years is of little importance, because most of the victims are steeped in an illicit underworld and, so the argument implies, are deserving of their fate.

The cartels infiltrate government and the security forces. They recruit some of the military's best soldiers to run their militias and to varying degrees, all levels of the police, local, state and federal, are in their pockets - how else to explain the recent seizure of $US15 million from a cartel convoy without a single arrest? How else to explain the discovery during a spot check on an Acapulco prison last month of two peacocks, 100 fighting cocks, dozens of TVs, two sacks of marijuana and 19 prostitutes?

The cartels are at war with one another, the authorities or both. Since 2007, 310 mass graves have been uncovered across Mexico - they contained 1230 bodies. Most of the 200 bodies recovered in one of the pits were innocent would-be migrants to the US from Mexico and South America.

Ironically, the cartels had paused to consider if all this bloodletting was in their own interests. When they decided in 2007 to attempt a negotiated carve-up of the Mexican drug turf, it was to Acapulco that the cartel capos repaired, convening in lavish surroundings at Las Brisas resort. The summit failed.

Acapulco - population 700,000-plus - is two cities in one. A narrow strip, between the Pacific sheen and the cockscomb peaks of the Sierra Madre del Sur, is reserved for tourists.

East of the ridge line are the slum quarters for ordinary Mexicans who wait on the tourists. But the resort city's status as Mexico's oldest drawcard has become its Achilles heel.

''Thirty years ago there was no Cancun; 20 years ago there was no Los Cabos, no Puerto Vallarta,'' says Arturo Martinez Nunez, the public face of a new campaign to rid the city of its narcotics scourge.

Compared with these newer resorts, he explains, Acapulco is doubly disadvantaged. Almost totally dependent on tourism, it has little cushion to absorb the impact of any slump in tourism; and to the extent that the others are controlled by cartels, they are dominated by single organisations and so are spared the brutality of the inter-cartel turf wars.

That double whammy is in play in Acapulco. By night, restaurants and bars on what should be the teeming Boulevard La Costera are deserted - despite or because of a heavy police and military presence in the streets. By day, rows of umbrellas and plastic chairs on the beaches are empty. The seafront bungee jump seems to have been mothballed. Only thin crowds watch the storied divers, young men who walk spider-like up a near-vertical cliff to plunge 50 metres into a tiny ocean channel below the Hotel El Mirador. Most of the Mexicans brave enough to come to Acapulco stay hidden in their secured resorts.

Local drug sales, made through hundreds of tienditas, or little stores, are lucrative. But the real prize for the cartels is control of the port through which cargoes of cocaine from Colombia and Peru arrive, to be dispatched overland to the US and on to Canada.

Until 10 years ago, the most powerful cartel in the country - the northern-based Sinaloa - had exclusive control of Acapulco. Today, another two big cartels compete, the Gulf Cartel and La Familia Michoacana, which itself has ruptured since the death last year of its leader.

In 2008, the Beltran Leyva Organisation split bloodily from what had been a long-standing co-operative arrangement with Sinaloa, claiming Acapulco as their own. In a December 2009 shootout, the authorities killed BLO leader ''el Jefe de Jefes'' Arturo Beltran Leyva, and the cartel's ranks divided again. (But they still avenged their leader's death. After the funeral of a Mexican Army commando who died in the shootout, the dead soldier's family home was attacked and his mother, sister, aunt and a brother were murdered.)

Flamboyant BLO henchman Edgar Valdez Villarreal challenged Beltran Leyva's brother Hector for control of the cartel. An American dubbed ''La Barbie'' because of his shock of blond hair, Villarreal rebadged his operation as the Independent Cartel of Acapulco.

He reportedly moved Colombian cocaine to the US at a rate of nearly two tonnes a month for an annual return of $US130 million. Hector Beltran Leyva attempted to reassert his family's authority as the South Pacific Cartel.

Another gang that emerged took a name that reflected its violent intent - La Barredora, or the street sweeper.

Villarreal's luck ran out when the authorities captured him in August last year, after deadly shootouts between the gangs and or the authorities up and down the beachfront. The deadly toll kept rising: April - six dead, including two schoolchildren; June - 3000 shots said to have been fired and dozens of grenades detonated, leaving 18 dead in the middle of the hotel zone; August - 14 bodies on a highway overpass.

A succession of gangsters who attempted to fill La Barbie's shoes did not last long. In August this year, Moises ''El Coreano'' Montero Alvarez was arrested and accused of ordering more than 40 deaths by decapitation and dismemberment.

His successor, ''El Comandante'' Gilberto Castrejon Morales, and five cronies were captured after a brief gunfight with federal agents in a suburb called Colonia Sabana earlier this month.

Endless infighting did in the BLO, but it was also assumed the bosses of the Sinaloa, Gulf and Familia cartels tipped off the authorities, who rounded up dozens of key figures in the remnants of Villarreal's cartel and Hector Beltran Leyva's operation.

This northern summer Acapulco seemed a hopeless case. The August tally of 150 murders put the resort city on course for an annual toll of 1000 killings, causing tourist numbers to plummet.

During a week-long visit this month The Saturday Age saw just a handful of foreign tourists. Occupancy rates for hotels and resorts last year reportedly were 48 per cent, compared with 70-plus per cent in the year before the government crackdown.

A glimmer of hope for Acapulco emerged in September, in an unlikely challenge to the cartels. It was not the city authorities, but its teachers who made a stand. Faced with threatened kidnappings and attacks on schools unless they paid half their salaries to the cartels in return for their ''protection'', the teachers shut more than 120 schools, saying they would return to work when authorities stood up to the cartels.

Sitting in his shoe-box sized office the secretary of the teachers' union, Nicholas Robels Pineda, brushes aside questions about the teachers' courage in being the first to stand up to the cartels, by reducing the equation to a simple economic argument - ''our teachers don't earn enough to be able to pay half to the Independent Cartel of Acapulco,'' he says. ''We couldn't pay a single peso.''

When The Saturday Age proposes taking his picture, the union secretary recoils. ''You publish my picture and tomorrow I could lose my head and this,'' he says, clutching a hand to what some American males describe as their ''package''.

The schools were a new target for the cartels, who eyed the teachers' government-funded salaries as easy pickings. Previously, their victims were those in the city and suburbs who could most easily monitor the movement of people - bar owners, petrol station and tyre service centre workers and taxi drivers, who hope that providing information to stand-over gangs might put a brake on the dollar amounts demanded by the cartels for ''protection''. But serving one cartel made them targets of the others, so much so that by August this year, a local newspaper had tallied the murder of more than 40 taxi drivers.

Understanding the courage of the teachers requires a sense of how the cartels punish any who cross them. In a bid to be seen to be more menacing than a regular gang of murderers, one of the cartels took to dismembering its victims, and then to leading the authorities on a macabre hunt by distributing as many as 27 parts of the same body across the city. A gunnysack found on a city footpath, near a school, contained five human heads.

Another cartel resorted to removing the faces of its victims and hanging them from posts. Later, the cartel took to cutting away the entire skin from some of its victims' bodies.

The city's chief forensic pathologist, who keeps a pistol in his desk drawer, seems to enjoy shocking visitors by flipping open a laptop filled with monstrous images of the cartels' knife work. Without warning during our interview, Dr Keynes Garcia Leguizamo clicked through some gruesome photos.

On a tour of the mortuary, the 29-year-old pathologist says that having just 25 bodies stored in his refrigerators is proof the tide of violence is turning. But he also reveals a shocking statistic - so far this year he and his team have reconstructed 50 bodies that had been delivered to the mortuary in varying stages of dismemberment. ''They come in garbage bags and we try to put them together before the families see them - but we can spend only two or three hours on each case.''

There are days when up to 100 families descend on the mortuary, demanding news about missing relatives. At the same time, many corpses go unclaimed, in some cases because the extent of the mutilation renders then unidentifiable. So far this year, more than 130 unidentified murder victims have been sent to a common grave about two hours' drive from the city.

By the time the teachers called ''enough!'' the murder tally for the year was about 900. Confronted by their refusal to return to the classroom, the authorities pledged a campaign for all of the state of Guerrero that would combine multiple forces under a single command - including almost 5000 members of the federal, state and local police, the military and the navy. Operation Secure Guerrero was launched in October.

''The idea was to retake control of the streets of Acapulco by reducing the violence,'' says Arturo Martinez Nunez, producing what he calls a heartbeat graphic - the murder data for 58 days before and after the start of the campaign. It shows the murder rate dropping from 3.6 a day to 1.6 a day.

''Two months ago the streets were empty. There was a collective psychosis, but now we are taking back the night - for locals and for tourists. We've got kidnappings and beheadings down to zero and the goal is to have zero murders by the end of December.''

The Saturday Age has been advised to treat the data cautiously, because when the military has spearheaded campaigns in other parts of the country, the level of violence had dipped but only for as long as the military remained in the face of the cartels. So despite the local claims of success, it is too early to read the Acapulco tea leaves.

There is also speculation the all-powerful Sinaloa cartel, headed by Forbes magazine world's-richest list nominee Joaquin ''El Chapo'' Guzman, might have wrested back control of the city.

President Calderon has invested hugely in this war. The ranks of the federal police have tripled to more than 53,000 since 2005. More than 30,000 new or retrained federal police are deployed and prison capacity has doubled. In 2006, Calderon promised military intervention as a temporary solution and a US congressional research service report from early 2008 quotes the Mexican President's prediction that it would take at least two years ''to take back control of Mexico''.

Calderon, however, remains defiant. Marking the fifth anniversary of his campaign earlier this month, he declared: ''We're going to continue defending the citizens until the last day of my term. Those who say it would have been better not to confront the criminals are completely mistaken - if we hadn't done this, they would have advanced in our communities and our institutions.''

That, and other oblique statements, amount to an acknowledgment that the cartels have morphed into a Taliban-like insurgency.

With a surge in marijuana and heroin production even as the authorities engage the cartels in urban war, the conduct of Calderon's forces and their limited success has earned harsher critiques.

In a new 214-page report, the New York-based Human Rights Watch concludes: ''Since the outset of Calderon's 'war on drugs', violent crime has skyrocketed; abusive policing has undermined the investigation and prosecution of criminal suspects; and widespread abuse and corruption has antagonised civilians who otherwise could provide security forces with crucial information. Homicides tied to drug violence have increased every year since [Calderon] implemented his public security strategy. Moreover, claims by the government that public security operations have been effective in reducing crime … are not borne out by the data.''

The first five years of the President's war have caused the cartels only to fracture, not to disappear. And increasingly, those that fail to win control of the drug smuggling then resort to extortion, kidnapping and racketeering.

Last year, the government claimed to have captured or killed more than half of almost 40 kingpins on its most-wanted list, but the violence and the drug running continue unabated, amid speculation that the limited success of the authorities is more to do with treachery in the ranks of the cartels than with good intelligence and forensics by the authorities.

Speaking on the sidelines of an industry function at the spectacular Zebu Restaurant, the city's Tourism Secretary, Erika Lorena Luhrs, volunteered that occupancy rates varied in the different markets, but the current average was just 28 per cent. As guests sipped chocolate margaritas, with the glasses rimmed with lime-infused chilli, Luhrs brushed aside the foreigners who account for about 20 per cent of the market, predicting a Mexican-led recovery.

Insisting that Acapulco was as safe as many other international destinations, there was a glib touch: ''Drugs are not a problem, because most people in the cartels are dead or in jail. The people who now direct the cartels don't have the Colombian contacts to get the drugs.''

Halfway up the mountain, the priest at La Garita, Father Reyna, emerges from his church of slabbed concrete after morning Mass attended by a congregation that is almost entirely female.

''The drug mafias have weakened the power of the city,'' he says. ''Families in my parish lose parents and young boys. They refuse to leave their homes and they are made to pay protection. They are afraid. Personally I know 16 people who are paying protection and, I know the family and friends of almost 20 people who have been dismembered in the five years that I have been here.

''You can say that we're holding our breath.''

Paul McGeough is chief correspondent.