Dr. William J. Fellner, 78, a former member of the Council of Economic Advisers and an economist who earned an international reputation for his work on inflation, full employment and related questions, died yesterday at his home in Washington after a heart attack.

Dr. Fellner, an advocate of free economies, was appointed to the three-member CEA by President Nixon in 1973 and served until 1975. He brought with him formidable academic credentials. He was the Sterling professor of economics emeritus at Yale University, where he taught from 1952 to 1973. He taught at the University of California at Berkeley from 1939, when he came to this country from his native Hungary, until he went to Yale. He was the president of the American Economic Association in 1969 and the author of numerous books and monographs.

A dilemma to which he addressed himself in recent years as well as earlier in his career was how to achieve full employment without unleashing ruinous inflation. This has been one of the most difficult economic problems facing the country since World War II. It remains unsolved.

Through the 1970s, attempts were made to keep employment high by increasing government spending and rapidly expanding the amount of money in circulation. Although the labor force grew, unemployment rates remained high. But inflation, fueled by spending policies and spurred by oil and food price shocks, reached double-digit figures.

Beginning in 1979, the Federal Reserve Board under chairman Paul Volcker began restraining the money supply to combat higher prices. The result was the hardest recession since the war and the highest unemployment rate since the end of the Great Depression.

With a civility and courtliness for which he was widely known, Dr. Fellner argued that the Federal Reserve Board, Congress and the White House could set a course in which market forces themselves would provide jobs without undue price increases. He rejected wage and price controls and other devices that impinge on free markets.

His basic views, set forth in numerous papers, speeches, books and articles, were that the Federal Reserve should set limits on the money supply that would inhibit inflation without causing severe unemployment. The government, investors and even individual households would be forced to make decisions on how to spend within the broad framework for economic growth laid down by the Federal Reserve.

In the last year, Dr. Fellner had criticized the Fed for seeking faster economic growth than he believed was consistent with a continuing reduction of inflation. Other economists argued that the policy he advocated, while containing price increases, would keep unemployment at unacceptably high levels.

At the same time, Dr. Fellner supported the indexing of taxes to inflation rates, a part of President Reagan's economic program that has been enacted but which has not yet gone into effect. Indexing adjusts taxes to the real earning power of taxpayers. As it is now, in times of high inflation, nominal incomes go up. People find themselves in higher tax brackets even though their purchasing power has stayed the same or even declined. The government, on the other hand, can count on these increased revenues to pay for its operations.

In Dr. Fellner's view, indexing not only would protect the individual taxpayer, but also would force the government to make harder choices on the programs it wishes to pursue.

Some economists in the government and private sectors contend that because of the enormous federal deficits foreseen for the next several years tax indexing should be repealed.

Herbert Stein, the chairman of the CEA during Dr. Fellner's service on it, said in a tribute yesterday that his colleague "in recent years. . . contributed greatly to the idea that inflationary policy could not solve problems of real output, employment and unemployment. The private sector would inevitably figure out what the government was doing and the period during which the real economy responded to inflationary policy would become shorter and shorter. The continued attempt to manipulate the economy by inflation would lead to price and wage controls and the end of the free economy. . . . He helped to impress these ideas on policy makers."

Dr. Fellner was born in Budapest. He was educated at the University of Budapest, the Federal Institute of Technology in Zurich and the University of Berlin, where he took his doctorate. He was engaged in a family business in Hungary until coming to this country in 1939. He became a U.S. citizen in 1944. Since leaving the CEA, he had been a resident scholar at the American Enterprise Institute and project director of its "Contemporary Economic Problems," a yearly publication.

His numerous books include "Monetary Policies and Full Employment" (1946), "Trends and Cycles in Economic Activity" (1955), "Probablility and Profit" (1965), and "Towards a Reconstruction of Macroeconomics: Problems of Theory and Policy" (1976).

Dr. Fellner's survivors include his wife, Valerie, of Washington; a daughter, Anna V. Thomas of Ann Arbor, Mich., and a grandchild.