An old-fashioned political deal struck between two powerful Democratic senators about a year ago could have broad consequences for whomever is elected president next year.

If the Democrats retain control of the Senate, the deal would mean that Sen. Daniel K. Inouye (D-Hawaii) is probably the next majority leader. The position is vital to any administration's hopes for success, particularly if the president and majority leader are in opposite parties. The majority leader effectively rules the Senate, dispensing perquisites, making committee appointments, scheduling floor debates and either expediting or bottling up legislation.

The incumbent, Sen. Robert C. Byrd (D-W.Va.), won the post in 1977, but became minority leader when the Republicans began their six-year control of the Senate in 1981. Late last year, after the Democrats regained control, Byrd ran again for majority leader -- and needed help. That's when the deal was cut, according to knowledgeable senators and other Capitol Hill sources who confided in Dale Van Atta.

Byrd faced two potential challengers in the secret vote: Inouye and Sen. J. Bennett Johnston (D-La.). Johnston had collected many IOUs by campaigning diligently for Democratic Senate candidates and soliciting corporate political action committees for contributions on their behalf. But Inouye, hard-working and well-liked by his colleagues, was the man to beat.

So Byrd went to Inouye, who had just won his fifth term, and made him an offer: If Inouye would support Byrd for majority leader this time, the West Virginian would step aside in 1989, leaving the post open for Inouye. As a sweetener, Byrd offered to let Inouye pick the new Senate sergeant-at-arms. Inouye accepted the offer.

Byrd was gambling that Sen. John C. Stennis (D-Miss.), the octogenarian chairman of the Appropriations Committee, would decide not to seek reelection in 1988 -- as indeed he has recently announced. As next in seniority, Byrd would step up as chairman, a post almost as powerful as the majority leadership he would have to give up.

The long-range part of the Byrd-Inouye deal has been kept quiet. Many Senate observers thought the payoff for Inouye's support was simply Byrd's appointment of Henry K. Giugni as sergeant-at-arms, a powerful position that oversees more than 1,000 staff appointments. Giugni was Inouye's administrative assistant, and was with Inouye before he came to the Senate in 1963.

There was another payoff for Inouye's support: Byrd named him to the prestigious chairmanship of the Senate Iran-contra committee. It gave Inouye national prominence and the opportunity to demonstrate fairness and bipartisanship that would help him in his quest for the majority leader's job.

Byrd and Inouye both duck questions about their gentlemen's agreement. When asked point-blank recently, Byrd did not deny a deal had been made; he merely smiled. However, he did acknowledge that he was "confidentially considering" replacing Stennis as Appropriations chairman in 1989.

Inouye didn't deny a deal, either. But he implied that his support for Byrd was out of friendship and respect, not because of a deal.