One of the largest guarantors of college student loans has asked for federal assistance in resolving what the Education Department has described as "serious financial problems."

The Higher Education Assistance Foundation, based in Overland Park, Kan., asked the department in recent weeks to approve a merger with a smaller agency in Nebraska to solve cash shortfalls. The Kansas agency, known as HEAF, carries $9.6 billion in loan guarantees on its books and is the agency designated to insure student loans in the District of Columbia.

Under three federal programs, private banks make college loans, which are insured by one of 55 guarantee agencies. The government in turn reinsures the guarantee agencies against student defaults, which currently approach $2 billion a year. There is a guarantee agency designated for each state, while several agencies, including HEAF, do business in more than one state.

Banks that make student loans have been concerned about the ability of guarantors to reimburse them for defaulted loans. Any financial failure of the agencies could make some banks less willing to make student loans.

Philip R. Rever, a vice president in HEAF's Washington office, said it is operating normally, with local banks getting reimbursed for defaulted loans yesterday as they are every Monday. The HEAF official said student borrowing should not be affected at District banks.

HEAF's problems, reported in the Wall Street Journal yesterday, triggered a sharp decline in the stock of the Student Loan Marketing Association. The decline -- $4.125 per share to close at $49.875 -- was widely cited as a factor triggering an overall market plunge.

Sallie Mae, as the federally chartered corporation is known, buys student loans, thus providing new cash for lenders to make more loans. It owns a number of HEAF-guaranteed loans, and has also extended an $865 million line of credit to the guarantee agency.

Sallie Mae officials spent much of the day seeking to calm investors' fears. "We are expecting that the situation will be resolved to the effect that there is virtually no cost to Sallie Mae," a spokeswoman said. She said the line of credit is secured by high-quality collateral such that "we have no material exposure whatsoever."

Experts outside the company said they believed that the company's losses, if any, would be minimal. "Sallie Mae is pretty cautious, to the point of irritation in the lender community," said one.

In a statement issued last Thursday, the Education Department said HEAF had notified officials of "serious financial problems." The statement, intended to reassure banks, said the department was "closely monitoring" the situation and "considering options" that "will ensure the availability of new loans and the continuation of guarantees and claim payments on outstanding loans."

Yesterday Etta Fielek, department spokesman, said officials expressed "very great problems" with the HEAF proposal for a consolidation with the Nebraska Student Loan Program Inc., a newer and much smaller agency with cash reserves of $2 million. Fielek quoted undersecretary Ted Sanders as saying the merger would be "like an ant swallowing an elephant."

Rever said that another option would be for HEAF to borrow funds from a private lender to meet its cash needs and then have the government insure that loan.

HEAF's financial difficulty resulted from too many defaulted loans made to students attending for-profit trade schools. Because of the high default rate, HEAF gets only 80 percent of the loans' value from the government, but the guarantee agency must pay banks 100 percent.

Guarantee agencies became part of federal student loan programs in the 1970s after some banks dropped out because they found government officials unresponsive. Studies also found more banks participated in states with guarantee agencies that handled state loan programs.