ALBANY — It was not a good week for New York’s cities and counties.

On Monday, Rockland County sent a delegation to Albany to ask for the authority to close its widening budget deficit by issuing bonds backed by a sales tax increase.

On Tuesday, Suffolk County, one of the largest counties outside New York City, projected a $530 million deficit over a three-year period and declared a financial emergency. Its Long Island neighbor, Nassau County, is already so troubled that a state oversight board seized control of its finances last year.

And the city of Yonkers said its finances were in such dire straits that it had drafted Richard Ravitch, the former lieutenant governor, to help chart a way out.

Even as there are glimmers of a national economic recovery, cities and counties increasingly find themselves in the middle of a financial crisis. The problems are spreading as municipalities face a toxic mix of stresses that has been brewing for years, including soaring pension, Medicaid and retiree health care costs. And many have exhausted creative accounting maneuvers and one-time spending cuts or revenue-raisers to bail themselves out.