In arguably the biggest crisis since its creation in 1975, the Convention of Scottish Local Authorities (Cosla) is being deserted by around half-a-dozen Labour councils which together provide services to about 1.5 million people.
The Sunday Herald understands that Glasgow, Inverclyde, Renfrewshire and South Lanarkshire are expected to serve Cosla with notices to quit in the coming weeks.
Dumfries & Galloway and Aberdeen City councils have already given Cosla the statutory year's notice of their intention to leave the umbrella organisation at the end of March 2015.
A break-up could affect budgets for services, as Cosla negotiates the overall funding package for local government with the Scottish Government, and also negotiates collective wage deals for around 250,000 council staff.
It could also see more fighting between Labour councils and the SNP Government ahead of the independence referendum.
Glasgow is already working on plans for a stripped-down alternative body, with no headquarters or permanent staff, which could act for it and other breakaway councils in negotiations with ministers and trades unions.
The leaders of Glasgow and South Lanarkshire councils discussed options last week.
A well-placed source in Scotland's largest council said: "Glasgow is going, and is already developing a model for what will replace Cosla."
The dispute has been simmering for months.
Because it runs 16 of the 32 councils, Labour has half the votes in Cosla's prime decision-making body, the monthly leaders' meeting, enabling the party to block any proposal it dislikes.
Last September, Labour used its clout to block changes to the funding formula for councils which could have cut spending to Labour areas, infuriating councils run by other parties who felt they had been unfairly shortchanged.
In retaliation, Independent, Conservative, Liberal Democrat, and SNP forces in Cosla started a review of the group's constitution to dilute Labour's influence.
A key idea is to downgrade the leaders' meeting and hand big decisions to Cosla's quarterly convention, which is based on delegates, and where Labour can be out-voted by other parties. The review of Cosla's constitution is expected to report its findings in the summer.
However, even the possibility of losing their grip on Cosla has so angered some Labour councils they are now threatening to quit.
Dumfries & Galloway Council voted last month to give notice to end its £110,00-a-year membership, with the proviso that it might change its mind after the review reported.
When Aberdeen City followed suit on Thursday, Cosla insisted the organisation remained strong.
However, the Sunday Herald understands that more Labour councils, working in concert, also plan to serve notices to quit in the coming weeks, putting a question mark over Cosla's future.
Cosla sources hope the threat of a breakaway group is a high-pressure negotiating tactic designed to preserve Labour's control.
However, one senior council source insisted the move was no empty threat. Even if the constitutional review changed nothing, Cosla was still doomed because of the ill-feeling now inside it, the source said.
Another council insider said there had been growing unhappiness with Cosla's failure to stand up for local government since the SNP won its Holyrood majority in 2011.
Stephen McCabe, leader of Inverclyde, said: "Our Labour group is minded to follow the lead of Dumfries & Galloway."
Renfrewshire boss Mark Macmillan said: "People trying to diminish the power of the leaders' meeting in Cosla have created a problem. Cosla's constitution was not an issue before Labour was in control of 16 local authorities."
A Cosla spokesman said: "The reality is that Cosla is the only local government association in the UK with a 100% membership. This will continue to be the case for the rest of this financial year and all of next financial year.
"During this time the organisation will be doing its absolute utmost to ensure that we resolve the issues that have been raised with us, as well as representing our full 32-council membership."