It's only a matter of time before a Welsh council goes bankrupt unless cash pressures ease, bosses have said.
Anthony Hunt, Labour leader of Torfaen council, said "the very fabric of our local public services is under threat".
And Mark Pritchard, independent leader of Wrexham council, said it faced cutting community care help that would have a negative impact on NHS services.
The Welsh government said it would continue to work closely with councils to "meet the shared challenges".
"We are struggling," said Mr Pritchard.
"A local authority across Wales.... will go bankrupt if we're not funded. It's only a matter of time."
He told BBC Radio Wales' Sunday Supplement that it had made £60m in budget cuts and more savings would be needed next year.
"It's only a matter of time before an authority across Wales will go bankrupt," Mr Pritchard added.
He said his authority is considering axing a £1.4m grant which fits home adaptions like hand rails, stairlifts and walk-in showers to enable people to leave hospital after a fall.
"That will have an impact on the health service," he said.
In August, BBC research found Welsh councils expected a combined shortfall of £394.8m over the next two years.
Mr Hunt said: "Sooner or later, if you stretch the elastic out every year, something goes ping - and I think we're reaching that point."
He highlighted the financial situation over the border where leaders claim that one in 10 councils in England could go bust.
"I think we're in a slightly better position here in Wales thanks to the work we've done with Welsh government, but those services are under threat," he said.
Mr Pritchard questioned some Welsh government spending priorities, from buying Cardiff Airport to offering universal free school meals.
"There's millionaires in Wales who have free prescriptions and their children can have free school meals - it's got to stop," he said.
"You can't give away everything."
The Welsh government said it was providing increased funding for local authorities this financial year, with a 7.9% increase across Wales on a like-for-like basis, following a 9.4% increase in 2022-23.
"But we recognise that local authorities are facing difficult decisions and we continue to work closely with councils to meet the shared challenges we face," it said.