Two months after moving into the State Department, some of the closest aides and advisers to the new secretary of state, Edmund S. Muskie, continue to be uneasy and suspicious about relations with President Carter's national security affairs adviser, Zbigniew Brzezinski.

These aides claim that they are more concerned about the problem than is Muskie. But they believe that the situation, unless rectified by Carter, is potentially damaging not only to U.S. foreign policy but to Democratic Party politics in an election year.

The latest irritation in the Muskie camp grew out of what one top adviser viewed as the "incessant" background briefings given by Brzezinski to the press and other officials on the trip to Europe and the Venice summit last week by the president and secretary of state.

The aide said these frequent briefings, in his view, create a problem "because it is unclear to those listening whether the views represent Brzezinski or the president. And since the president never disavows them, it raises a question in people's minds when there is a discrepancy [between Muskie and Brzezinski] and makes it appear that Muskie is speaking for the president and the administration."

While there are substantial areas of agreement betweeen the two men, Muskie aides and some senior State Department career officials say there is also "a real difference of view between Brzezinski and most people in this building on some fundamental issues." This is especially so on questions of how to deal with the Soviet Union and U.S. allies.Brzezinski almost always takes a harder line.

This is also especially important, some officials believe, because it seems to them that the president, himself does not hold strong, fundamental views on some of these subjects.

Last Wednesday, one of Muskie's closest advisers and long-term associates, Washington lawyer Berl Bernhard, mentioned his concerns about Brzezinski's role in foreign policy in relation to Muskie's during a meeting with Robert Strauss, head of the president's reelection campaign.

Bernhard, who managed Muskie's 1972 cammpaign for the presidency and now serves without pay as a part-time adviser, also has mentioned these same concerns recently to John C. White, chairman of the Democratic National Committee.

Problems between the top-level officials at State and the powerful adviser working directly for the president in the White House basement are now new. Indeed, the dual power centers have flourished alternately in the Nixon and Carter administrations.

The current situation, however, is somewhat different because of the strong personality and allegedly quick temper of the new secretary of state and the fact that Muskie, who spent 22 years in the Senate, is a major figure within the Democratic Party, especially within the liberal wing.

Thus, another of Muskie's top aides argues privately that if differences between Muskie and Brzezinski should unexpectedly and publicly get out of hand, it could hurt the president within his own party by undoing much of the political good will that was achieved by the appointment of Muskie in the aftermath of Cyrus Vance's resignation as secretary.

"It is more of a problem for the president than for the secretary," says one Muskie adviser. "Muskie has a following. Brzezinski does not."

Strauss brushed off the whole business, relegating differences to natural bureaucratic problems that have always been part of those two jobs.

"Muskie wants to be a good secretary of state and help the president get reelected," he said, indicating he believes that neither official is likely to let things get out of control between now and the November election. l

Nevertheless, differences between Vance and Brzezinski and concern over the administration's seeming to talk with two foreign policy voices was a frequent characteristic of the 3 1/2-year secretaryship of Vance. Some Muskie aides believe it is continuing, even though Carter, when the new secretary took over, said Muskie would be "the chief foreign policy spokesman for the administration."

"There is no question that there is a feeling of uneasiness among the people around Muskie," says one State Department official. "There is obviously hypersensitivity up there" to being upstaged by Brzezinski.

"Brzezinski is hard for them to deal with. He's experienced, knows the issues, explains things well, has been around for 3 1/2 years, and is close to the president," one says.

Aside from Muskie's newness to the world of diplomacy and administration infighting, many of the secretary's personal aides also came with him from Capitol Hill or private life and also are inexperienced in such situations.

Indeed, within the White House, some officials believe it is the inexperienced foreign policy aides and advisers around Muskie who are creating more problems than would normally be the case.

Like the secretary's aides, these officials also have the feeling that Muskie is personally less concerned about the situation than those around him. m

But his advisers and aides, a White House official claims, "are trying to take control of the process and they don't know how, nor do they know how the whole foreign policy-national security apparatus operates in the executive branch."

One official claims State has developed a "we're-going-to-show-'em attitude" toward Brzezinski's National Security Council staff.

Sources claim that on two occasions recently important White House policy papers on the strategic arms limitation treaty with Moscow and the Soviet invasion of Afghanistan came back from the top level at the State Department in a form "unrecognizable" from what had been sent over there after being passed upon by the NSC, Pentagon, joint chiefs of staff and some senior State Department officials.

Unhappiness over what some White House officials see as a potential breaking down of this interagency system established by the president extends to the Pentagon and the joint chiefs of staff, sources say.

One senior official claims that in contrast to concerns over whether Brzezinski is upstaging Muskie in public or getting in too many newspaper pictures, Brzezinski could produce a list of offenses committed by the Muskie people. Also, the official says, both Brzezinski and Defense Secretary Harold Brown have been rather patient as Muskie and his staff feel their way into the pattern of the administration.