It is a problem common to many administrations: the lame-duck Cabinet.

By most accounts, it's a very frustrating proposition. And, in the case of the Reagan administration, the situation has been intensified by recent changes involving four new secretaries.

"The problem is larger than these new Cabinet secretaries," said Ed Rollins, President Reagan's former White House political director. "In the last year, you run out of gas . . . . It's not a good time for new initiatives. The civil service types know there's going to be a change. Everybody starts watching the clock. A year from now there will be a new president who may not have the same agenda."

The most recent Cabinet shifts include:Defense: Frank C. Carlucci, the president's national security adviser, nominated yesterday to succeed Secretary Caspar W. Weinberger, who resigned because of his wife's health problems.

Labor: Ann Dore McLaughlin, nominated Tuesday to succeed Secretary William E. Brock, who resigned last month to manage the campaign of Senate Minority Leader Robert J. Dole (R-Kan.) for the 1988 GOP presidential nomination.

Transportation: James H. Burnley IV, nominated last month to succeed Secretary Elizabeth Hanford Dole, who resigned to assist in her husband's campaign. Burnley was Dole's deputy.

Commerce: C. William Verity Jr., confirmed last month to succeed Secretary Malcolm Baldrige, who died July 25 in a California rodeo accident when a horse fell on him.

And in place for fewer than 11 months is Reagan's chief of staff, former Tennessee senator Howard H. Baker Jr., who has Cabinet status.

There are also new people in several jobs just below the Cabinet level. Former FBI director William H. Webster moved to the Central Intelligence Agency in May after William J. Casey, a longtime Reagan confidant, resigned for health reasons and then died. The new FBI director, William S. Sessions, was sworn in this week. At the National Security Council, Lt. Gen. Colin L. Powell was officially named yesterday by Reagan to replace Carlucci as national security adviser.

As an administration nears the end of its term, "It's unlikely there will be any major new initiatives or any major cutbacks," said Gordon Jones of the Heritage Foundation. "It's likely to be a standoff for the next year."

When the "attention of the political types is diverted elsewhere," Jones said, bureaucrats who disagree with the administration's objectives are "likely to lose papers and see that less gets done."

As a practical matter, Rollins said, "In the last year you have the phenomenon of a lot of assistant secretaries out looking for jobs . . . and it's a difficult time to be recruiting."

Even though a Cabinet secretary who comes in at the end of an administration may be superbly qualified, the nominee is rarely part of the president's inner circle and is often seen by the bureaucracy as an outsider intent on adding a new position to a resume.

"A good part of this is endemic to a lame-duck administration, and we're beginning to see that," said Norman Ornstein of the American Enterprise Institute. "It becomes more and more a caretaker mission . . . . And then it becomes very difficult to find the right kinds of people to fill the positions.

"There's always an opportunity at the margin to do a little something here or there," Ornstein said, "but it's a frustrating job, even though it's a good experience . . . and {the title of Cabinet secretary} is something you can carry around for the rest of your life."

He added that the phenomenon builds into a "ripple effect through the government" with even more serious resignations at the assistant secretary level and few qualified replacements willing to move to Washington for a short-term commitment.

"This will not be the end of it," Ornstein said. "We're going to see more changes in the next six months."

In the meantime, Rollins said, the best way for new Cabinet secretaries to handle the lame-duck syndrome is "to take three or four key areas and really try to stress those. Obviously, you can't go in with a total agenda.

"You try not so much to manage the department because it would be difficult to get on top of that. But you can try to push a few issues . . . and it's probably better to try to push your items externally than to try to push them internally through the bureaucracy," he said.

But Jones said he believes it may be better if the new officials do not try to accomplish much. "That's probably the best we can hope for. Almost anything that might happen is not that good. The media says we have to have a tax increase, and half the Senate wants a protectionist trade bill. That's all negative. From the point of view of conservatives, the idea that nothing gets done is not necessarily bad," he said.

Of the new Cabinet secretaries, only Carlucci -- who has had a long government career -- is generally considered to be enough of an insider and to have enough stature to be able to carry on much as his predecessor would have. "He knows what he's doing, and he'll be able to move on Weinberger's agenda," Rollins said.

Ornstein noted that Sessions, who has been confirmed to a 10-year term, and Webster will be able to carry on without hindrance because they generally "transcend" politics and have a well-defined sense of their mission, even at the end of an administration.

"Webster is not under the same constraints that a regular CIA director would have," Ornstein said. "He's a completely different figure from a Casey, who was basically a confidant of the president."

But Ornstein said he believes it will be difficult for the new Cabinet hands, who are not as well known, to "build up enough credibility" in such a short time to have a serious impact on policy in their departments.