Council debts and deficits in the Black Country, Staffordshire and Wyre Forest soared by almost £1.6 billion in a year.
And some now have financial liabilities that exceed the value of all the property and other assets they own, according to research by the TaxPayers' Alliance.
Councils say the figures are misleading because they also include the pension deficit as well as the cost of borrowing.
They are grappling with multi-million cuts in their grant funding and axe thousands of jobs.
Nationally the TPA found councils had more than £180 billion in long-term liabilities on 31 March 2013, an increase of eight per cent on the year before.
It said this was almost seven times the amount raised in council tax in that year, meaning revenues were being used to pay off debt interest, rather than fund essential services.
Its research showed that between 10 councils serving south Staffordshire, the Black Country and Wyre Forest, liabilities rose from a combined £5.4 billion to more than £6bn.
In Walsall, the liabilities were £758,116,000, compared with assets of £488,720,000. The TPA said this meant the council had liabilities worth 155 per cent of its assets.
Jonathan Isaby, chief executive of the TaxPayers’ Alliance, said: “It is nothing short of immoral for councils to pile further debt on the next generation. Britain’s public finances are in real trouble, and local authorities can no longer avoid tough choices by putting the bill on taxpayers' credit card. Councils must look again at overgenerous pensions and wage a war on waste, or Britain's debt burden may soon become too heavy to bear."
But Wolverhampton City Council's finance chief said the figures did not reflect the true picture.
Councillor Andrew Johnson said: "Our assets include things like the ring road and Queen Square and it's not as though we can ever sell those.
"The liabilities for Wolverhampton also include £551 million in the pension fund and it will be a similar picture for other authorities. That's only a problem if we had to pay every single worker their pension at the same time, which would never happen."
And Stafford Borough Council spokesman Will Conaghan said: "We are not saddling future generations with debt. The TPA figures include liabilities for pensions which are based on assumptions and this will not impact on the financial position of the council or council tax levels.
"In fact independent auditors commented that due to our prudent approach to treasury and financial management we are in a position that we do not need to take out high levels of borrowing to fund planned capital projects."
Phil Cooper, director of finance at South Staffordshire Council said: “This is actually a pension deficit issue, which is a national issue.
"Probably every council in the country has a deficit in their pension fund and we are required to show this in the liabilities section on council balance sheets."
"At South Staffordshire we have far less assets to offset the liabilities, creating a percentage deficit which is misleading as it is being compared with other, much larger councils.”
Thousands of jobs are being shed by councils to try to keep afloat following severe cuts in central government grants.