(left) Joel Player and Alan Wright will be amongst the first Australian same sex couples to tie the knot on the 7th of December in Canberra.

(left) Joel Player and Alan Wright will be amongst the first Australian same sex couples to tie the knot on the 7th of December in Canberra. Photo: Katherine Griffiths

When the clock strikes 12.01am on December 7, Joel Player and Alan Wright will exchange vows and cement their place in history as the first gay couple to marry on Australian soil.

This is the hope held by the north Canberra couple, who plan to marry in the first minute on the first day same-sex marriages can take place, if a High Court judgment does not prevent them from doing so.

Mr Player already considers Mr Wright his husband, after a commitment ceremony four years ago. However, he has waited years for the word ''husband'' to have legal recognition and he wants to be "at the frontier of marriage equality" if the court reaches a decision in the Commonwealth's case against the ACT government this week, and finds in the ACT's favour.

Family and friends are flying in for the ceremony, including Mr Wright's sister, whom he has not seen for 20 years. "We want this ceremony for the legal and social recognition," Mr Player said. "We're no longer going to be referred to as boyfriends.

"The hearing is on our minds to some extent but, either way, if it doesn't happen this time it will happen [eventually].'' The full hearing of the government's case against the ACT's recently enacted same-sex marriage law is due to be heard on Tuesday and Wednesday.

The Commonwealth is arguing that the federal Marriage Act gives an exhaustive and uniform definition of marriage and says that the ACT's new law is inconsistent with both the Marriage Act and the federal Family Law Act, which governs issues such divorce.

The ACT's legal team will argue that the Federal Parliament has failed to outlaw same-sex marriages and that the territory's law can operate concurrently with federal marriage laws.

Although the High Court may not make a finding in the case this week, the ACT government expects that it will do so before the first marriages take place on December 7.

Chief Minister Katy Gallagher said she was "desperately hoping" for a verdict in the ACT's favour and she criticised the federal government for behaving as though it had a "clear-cut" case.

On Sunday, a spokesman for federal Attorney-General George Brandis said it would be inappropriate to comment while the case was before the court.

"I certainly think the attitude of the Commonwealth that it's a very clear-cut case is not supported,'' Ms Gallagher said.

''It's certainly not supported by the legal advice of the ACT government. They genuinely advise it's impossible to predict.

"All these things get lost in legal arguments but, for me, it's just genuinely about people who want their relationships acknowledged.

"I hope desperately that the law will be upheld. The sky won't fall in. Life will go on," the Chief Minister said.

Glenda and Jennifer Lloyd are also among the couples planning to marry on December 7.

The couple, who have been together for 10 years, will tie the knot in the rose gardens at Old Parliament House.

"I'm trying to find a balance between optimism and not being so optimistic that I'm devastated if it doesn't happen," Glenda said.