The Securities and Exchange Commission, in its first securities-fraud case against a state, accused New Jersey of misleading investors about the health of its two largest state pensions while selling billions of dollars in bonds.

State authorities settled the case without admitting or denying wrongdoing.

While it singled out New Jersey, the SEC is conducting several investigations into what other states disclosed about their weakened finances.

States ranging from California to Illinois to New York have been thrown into financial difficulty by the economy but have been able to avoid disaster by selling bonds to investors, many of them individuals seeking safe, tax-free income.

States as a whole face a trillion-dollar gap between the pensions, health care and other retirement benefits they have promised to public employees, and the money set aside to pay the benefits, according to a report by the Pew Center on the States. The SEC said it is concerned about how these problems are disclosed to investors.