They are generally seen as ideologically closer to Labor than the Liberals, but it is not without precedent for the Australian Greens to form an alliance with the conservative side of politics.
The Tasmanian Greens, under its then leader Christine Milne, supported a minority state Liberal government between 1996 and 1998.
A University of Canberra political scientist, Robin Tennant-Wood, said the Greens found it easier to work with the Liberals than they had with a previous minority Labor government.
''It was a lot more successful than the previous Labor-Greens accord … where Bob Brown clashed dreadfully with the Labor premier Michael Field,'' Dr Tennant-Wood said.
''People say the Greens won't negotiate with the Liberals but they have done and it can work.''
Labor formed a minority Government in Tasmania in 1989 under its accord with the Greens but the deal collapsed the following year.
The 1996 deal occurred despite the Liberals previously ruling out working with the Greens.
In recent years, Labor in Tasmania has overcome its reluctance to work in coalition with the Greens.
The present state Labor government includes two ministers and a parliamentary secretary from the Greens.
In the ACT's case, policy would be the key to any serious attempt by the Liberals to woo the Greens' support in the assembly, Dr Tennant-Wood said. However, she said she would be surprised if the Liberal leader, Zed Seselja, won the Greens' votes he needed to be elected chief minister.
''The Greens reiterated last night that they will take it on a policy-by-policy basis,'' she said. ''They're not going to dismiss the Liberals out of hand. I'll be surprised if they support the Liberals into government.
''I got the feeling from Zed Seselja's speech last night that he seems to think that because he's got eight seats the Greens will automatically have to support him. No, it doesn't work like that and Zed himself has spent the past four years insulting and ignoring the Greens in turn.''
Dr Tennant-Wood said there was a slim chance that the Greens would support Mr Seselja.
''But, if he comes up with a package of policies that's palatable to the Greens and they think that will advance their agenda, then, yes, they can do that.'' Peter Jean