WHEN IT CHOSE H. Robert Heller for the Federal Reserve Board, the White House was looking for a candidate with substantial experience in international finance. That was the right qualification. The Federal Reserve's work is now more than ever concerned with the international economic system, and its chief preoccupation currently is the falling exchange rate of the dollar. As the director of economic research at the Bank of America, and formerly chief of financial studies for the International Monetary Fund, Mr. Heller brings strength to the most demanding of the board's present responsibilities.

To replace the departing Preston Martin as vice chairman, the White House has nominated Manuel H. Johnson, an able economist who, until he joined the board last February, had been an assistant secretary of the Treasury. Here the question is whether the administration intends to signal renewed support for the supply-side theories with which Mr. Johnson was identified at the Treasury.

The politics of the Federal Reserve Board now revolves around inflation and attitudes toward it. People in the financial markets tend to weigh each appointment above all by that standard -- whether the appointee is committed to the lowest possible inflation rate, or whether he seems willing to run inflationary risks to speed up the growth of the national economy. The chairman of the board, Paul Volcker, has earned unusually high standing in the financial world by his success, over the past 6 1/2 years, in forcing inflation down.

As long as Mr. Volcker remains in office, the Reagan administration enjoys an unusual degree of freedom to run large deficits and, when it chooses, to hint at economic strategies with inflationary implications. The administration does not have to worry much about reactions in the financial markets, because the people there put their trust mainly in Mr. Volcker. But his term as chairman ends in August 1987. From now onward, discussion of Federal Reserve policy will increasingly be caught up in speculation whether the president will ask Mr. Volcker to remain for a third four-year term -- and whether, if offered reappointment, he would accept it.

What might a post-Volcker board look like? Because of the recent resignations, most of its members will have had less experience than has been customary in the esoteric and highly specialized business of central banking. The vice chairman's office has not traditionally been a path to the chairmanship, but the White House has handled Mr. Johnson's nomination in a fashion suggesting that he is at least a possible candidate. For the present Mr. Reagan evidently wants to continue to enjoy the advantages of Mr. Volcker's presence while, through the advancement of Mr. Johnson, offering a concession to the dissenters in his party. That sounds like a formula for continuing tension within the Federal Reserve.