George Bush often said in his campaign that his years of service and travels abroad, even for funerals, made him the candidate of experience in foreign affairs and the best qualified to lead the nation and the West in a dangerous and rapidly changing world.

But more than three months after his election, as Bush embarked on the first overseas trip of his presidency - to attend the funeral in Japan of Emperor Hirohito and to visit briefly with officials in China and South Korea - his administration was still struggling to assemble a foreign-policy team and find direction on a range of global problems.As a result of troubles in the State Department and the Pentagon, Bush's national security adviser, retired Air Force Lt. Gen. Brent Scowcroft has, for the moment, assumed the most influential role in the making of foreign policy.

Scowcroft grew up in Ogden, Utah before attending the U.S. Military Academy at West Point. He headed the National Security Council staff when Henry Kissinger was secretary of state. Expert observers, including former White House advisers, say he has filled the policy vacuum and also has moved toward a restoration of Kissinger's more traditional views of the Soviet Union and the Cold War, in contrast to the roller-coaster policies of the Reagan years.

Although Scowcroft has insisted that the national security adviser should be "an honest broker" who remains behind the scenes to coordinate the making of policy, his has become the most influential voice in arms control and U.S.-Soviet relations, sources said.

Scowcroft meets with Bush each morning to brief him on national-security policies and problems. Scowcroft also chairs the important "principals committee" of the National Security Council, a policy-making group that includes Cabinet officers and top military men.

His deputy, Robert Gates, the former second in command at the Central Intelligence Agency, chairs the security council's "deputies committee," which is made up of sub-Cabinet officials and which meets several times each week.

The delay in the confirmation of John Tower as secretary of defense and the absence of Pentagon representatives at the policymaking table have compounded the apparent paralysis of the administration in establishing even the outlines of its policies toward Europe and the Soviet Union, further arms reductions and the future of NATO, and the simmering conflicts in Central America and the Middle East.

But while Secretary of State James A. Baker III has been preoccupied with learning his new turf and putting his top staff together, and Tower has been fighting for his political life, sources say that Scowcroft's power and influence has grown.

Scowcroft already has appeared on television to set out his well-known, long-held views on the next steps in the modernization of the U.S. nuclear arsenal and arms negotiations with the Soviets.

Robert Hunter, a former member of the National Security Council staff who is now with the Washington-based Center for Strategic and International Studies said, "Scowcroft is having some staff problems, but his people don't have to go through the Senate confirmation process and he knows the subjects well himself. With Baker and Tower having their separate problems, it is clear that Scowcroft has been exerting his influence. And he is leading the Kissinger restoration."

"There was a great deal of discomfort with Ronald Reagan's policies toward the Soviets, which were depressive-manic, ranging from calling them `the evil empire,' to the euphoria toward (Soviet President Mikhail) Gorbachev," Hunter said. "The traditionalists want more predictable policies."

Scowcroft, along with Lawrence Eagleburger, who is to become the No. 2 man at the State Department, were in business with Kissinger in his international consulting company, which had as its clients a number of the world's giant corporations.

Robert D. Blackwill, the new National Security Council senior director for European and Soviet affairs, a former Peace Corps volunteer and foreign service officer who has been on the faculty of Harvard's Kennedy School of Government, is typical of the professionals Scowcroft has recruited.

Blackwill worked with and is an admirer of Kissinger. In one article, he denounced the Reagan administration for depending for its foreign policies on "ideological zealots" and "fumbling amateurs," and he called for a return to the sort of professionals Kissinger and Scowcroft appointed during the Nixon and Ford administrations.

Although Bush chose to make his foreign-policy debut in Asia, he has gone there without the services of an assistant secretary of state for Asian affairs, because Baker has yet to appoint one. Although Bush met in Tokyo with leaders of the West and the Middle East, the administration has not yet put into place the key State Department policy-makers for Europe, the Middle East or Latin America.