More than 8,000 current and former members of the Senior Executive Service should be getting back pay of up to $5,200 around Christmas under an agreement reached Tuesday between the government and attorneys representing the executives.

Most of the people scheduled to receive the checks live in the Washington area. They served in the elite service between October 1979 and October 1981.

The $31.5 million settlement represents portions of pay raises denied the executives because of pay caps imposed on federal workers by Congress. Current pay for the executives, ranging from $61,296 to $73,200 a year, will not change.

The settlement finally resolves a legal dispute initiated by a group of service members working at the National Labor Relations Board in Wisconsin. The U.S. Circuit Court in Milwaukee ruled in their favor, and after a series of appeals by the government, the Supreme Court effectively settled the issue by refusing to hear the case in April.

The decision grants back pay to executives in levels 4, 5 and 6 of the service. The Milwaukee court will decide in November whether executives in pay levels 1 through 3 are to share in the back pay, and if so, how much they get. Most executive service members are in pay levels 4 through 6.

Back pay is based on salaries being earned between October 1979 and October 1981. Payments will also be made to retired service members who qualify, or to the survivors of those who are eligible.

In some cases pensions of retired executives will be adjusted upward slightly, because government retirement benefits are based on length of service and salary.

Next month the court, using addresses supplied by the Office of Personnel Management, will send letters to eligible executives notifying them of the awards. That letter will include a verification statement that the executives must return by mail.

Executives who are not contacted by mid-September and who think they may be eligible for back pay are advised to write this address: SES Back Pay, P.O. Box 14047, Washington 20044.

Blair Childs, executive director of the Senior Executive Association, said that if "no hitches occur, affected executives should be receiving their checks by Christmas. But it is essential that they return a verification form . . . otherwise their payment may be delayed."