The State Department office of security paid $1.3 million in overtime to 135 of its 144 armed agents during the last fiscal year - an average of $10,000 apiece - and the figure is expected to rise to $1.8 million for the same number of agents this year, department figures show.

Officials at various levels agreed that the situation has gotten out of hand - despite the special working circumstances of agents who guard public figures - and said they are considering possible solutions.

The situation has created a group of agents who are "well-do", but overworked and financially over-extended, who earn the equivalent of their base salary and sometimes double or triple it in overtime," according to one State Department source.

"When they go out and buy a house, they ask the office to tell the bank they make, say, $16,000 in salary, but can count on making another $16,000 in overtime pay, so they are way over-extended," the source said.

The nature of the work and the long hours combine to cause ulcers, high blood pressure, possible drinking problems, and a high rate of marital difficulties, among other problems, the source said.

The armed agents who are assigned to guard visiting dignitaries such as those in the Arab-Israeli peace delegations, have been working such long hours - 12 or 14 hours a day, 30 or 60 days in a row - that some sources say theya re concerned about the effectiveness of the security and the physical and mental well-being of some of the agents themselves.

The recent rise in terrorist activities, the convening of the United Nations General Assembly, and the Arab-Israeli peace talks here all have contributed to a dramatic increase in the demands on agents' time, State Department officials said. The number of dignitary protection assignments has grown from 150 in 1976 to 238 so far in 1978 while the number of agents has remained the same.

John Thomas, assistant secretary for administration at the State Department, disputed allegations that he level of protection has become inadequate. But he said. "We are concerned about the long hours to the points that we have already started a review of the method of assignment" and the effects on the efficiency of agency.

But, he added, "I don't see any increase in staff coming."

The agents' base salaries range from about $13,000 to more than $30,000.

The Secret Service, which provides guards for visiting heads of state, has experienced similar problems with limited manpower and overtime, official said.

However, the Secret Service insists on using a much larger number of agents a much larger number of agents per assignment than the State Department provides, one source said. In fact, the source said, visiting heads of state have on occasion declined Secret Service protection because "they didn't want (so many) gunslingers, follow-cars, platoons of troops and flashing lights. They wanted the (much smaller number of) agents the State Department provided, so we gave it."

A Secret Service spokesman confirmed that there have been "a number of declinations" from various dignitaries, but said, "They didn't give reasons."

Other complaints from State Department sources centered on a duplication of functions by their own office and the Secret Service: while Secret Service handles heads of state, the State Department may be covering their wives and children in the same place, each from separate command posts, for example.

The issue has heated up in the wake of a congressional investigation into federal overtime pay practices. Investigators charge that government accounting systems have become so poorly managed and chaotic that they invite waste, abuse or outright fraud.

Cases of possible fraud at several agencies are in Various stages of investigation or prosecution by federal officials. The agencies include the U.S. Forest Service, Internal Revenue Service, Department of Transportation, and Health, Education and Welfare.

Rep. Glady's Spellman, chairman of the House compensation and employe benefits subcommittee, is scheduled to hold a second hearing on the subject today. Among those scheduled to testify are representatives from the departments of State, Defense, Justice, Housing and Urban Development and the Government Accounting Office.