THE FEDERAL RESERVE SYSTEM, over the past generation, has had three strong chairmen - Marriner S. Eccles, William M. Martin and Arthur F. Burns. Mr. Eccles's death last week recalls the long struggles between the Fed and the White House in the years just before and after World War II. The issues of that time are still alive today, especially with Dr. Burns's term as chairman now about to expire.

The Fed is almost a fourth branch of government, exercising its great power under a board of governors serving 14-year terms. An appointment to the Fed is a bit like an appointment to the Supreme Court: Once the nominee takes his seat, a President can no longer give him orders; he can only argue with him. By his choice of candidates, the President transmits a signal - and a important one - indicating his purposes in economic policy.

Mr. Eccles was a Utah banker who came to the administration's attention in 1933 with a speech endorsing deficit financing. He had begun to work out for himself the central ideas of modern fiscal management - a remarkable intellectual feat - at a time when they were hardly known, let alone accepted, in this country. President Roosevelt advanced the influence of those ideas when, the following year, he put Mr. Eccles on the Federal Reserve Board. But very shortly Mr. Eccles was publicly at odds with the administration over the independence of the Fed.

The issue returned, sharper than ever, after World War II when President Truman wanted the Fed to continue the wartime practice of holding up the price of federal securities. Holding up prices meant holding down interest rates, and it also meant turning the Fed into a subsidiary of the U.S. Treasury. In 1948 the President refused to reappoint Mr. Eccles chairman of the board. Why? Robert J. Donovan, in his recent history of the period, suggests that the reasons went beyond pure policy and Mr. Eccles's increasingly cautious views. As a Truman aide told Mr. Donovan, the White House felt that "in general, the Fed had too much power, that it should be cut down a notch . . ." Mr. Truman later remarked to his staff that he had wanted Mr. Eccles to know "who's boss." That was in character. But was the President right?

The country had just been through a great surge of postwar inflation, and Mr. Eccles was a strong advocate of anti-inflationary credit restraints. But 1948 was an election year, and economic growth was far from assured; as it turned out, the economy tipped into a recession a year later. The country needed more than an anti-inflation program.

As for the Fed today, Chairman Burns makes it pretty clear that he considers higher interest rates less of an evil than higher inflation. He has made himself a symbol of monetary restraint. He is accused of sacrificing jobs and growth to hold down prices. But he would probably reply that it's a false choice, since inflation will kill economic growth in any case. That argument is more formidable in today's circumstances than it was 30 years ago.

Does the Burns position represent a fundamental challenge to Mr. Carter? No one can really say. While Dr. Burns's intentions are clear, Mr. Carter's are not. His decision on Dr. Burns's reappointment is one of several - along with the budget and the tax bill - by which Mr. Carter is going to have to define his policies this winter. And if he replaces Dr. Burns, will he be right - as, on the whole, Mr. Truman was right in 1948? We can't answer that one until we see who, if anyone, is to succeed Dr. Burns.