The current adminstration formed as a result of the SNP becoming the single biggest party after May’s local elections, with seven councillors.
But the LibDem and Tory groups, who have six councillors apiece, have regularly voted down the administration.
Most recently they teamed up to vote through a controversial motion to cut council employees’ redundancy terms.
After the vote, Tory group leader Andrew Polson slammed the SNP’s “lame duck leadership”.
He added: “In particular, Councillor Low, as leader of the council, has shown on this issue and previously in others that he is incapable and not prepared to make decisions which will benefit all the people of this community. If he and his group cannot fulfil the role they should move aside and let others lead.”
The next full council meeting is on December 21 and the Herald understands it is likely that either the Conservatives or LibDems will take control, with the support of the other party.
Council leader Gordan Low said: “We took on the administration in good faith, seeking to carry forward a progressive anti-austerity programme in the interests of the whole community.
“However, that has always been dependent on the other groups acting constructively.
“Unfortunately, the LibDems and Tories, who were not prepared to take on the responsibility of administration, have chosen to work hand in glove, acting as a coalition in all but name to obstruct the work of the council and impose their own agenda. That’s not sustainable.
“We will seek to overturn last month’s decision at the next meeting, and invite the other groups to have a rethink about where they’re taking the council. That’s the choice they need to make.”