A retired Navy admiral and a two-star Army general, both of whom served under Alexander M. Haig Jr. when he was commander of North Atlantic Treaty Organization forces in Europe, are moving into key positions in the White House office of President Reagan's national security adviser.

The naval officer is retired Rear Adm. James W. Nance, who was sworn in as deputy assistant to the president for national security affiars in White House ceremonies yesterday. Nance will be second in command to the president's chief special assistant for national security affiars, Richard V. Allen.

White House officials also confirmed yesterday that Army Maj. Gen. Robert L. Schweitzer, who is still on active duty, will be joining the White House national security staff under Allen.

During much of the past decade, when Henry A. Kissinger held the White House adviser's post under President Nixon and when Zbigniew Brzezinski held it under President Carter, the office became extremely powerful, rivaling and frequently overshadowing the State Department as a spokesman for, a formulator of, U.S. foreign and defense policy.

President Reagan has made clear on several occasions, however, that he wants to end that rivalry, with the White House adviser serving primarily as a low-profile, backtage coordinator among State, the Pentagon and the White House, rather than as a policy-maker competing with them.

Though it is not unusual for active-duty or retired military officers to serve in the White House adviser's office -- Haig served on Kissinger's staff from 1969 to 1973 -- the movement of two officers who previously worked for Haig into those jobs now has inevitably touched off speculation by current and former White House staffers that the ex-NATO commander has a widening "network" of aides strategically placed within the new administration to ensure that no rival power center pops up again.

Nance, according to White House officials, was the senior naval officer on the staff of the commander of U.S. forces in Europe when Haig held the combined job of U.S. and NATO commander between late 1974 and mid-1979.

Schweitzer, currently working as a strategic planner for the Army in the Pentagon, is a former chief of the policy branch at NATO under Haig and also served on various White House national security committees when Haig worked for Kissinger.