At first blush, Walter Fauntroy's problems appear to be the kind that any politician would love to have. He is expected to easily win another term as the District's nonvoting delegate to Congress on Nov. 4. He breezed through the Democratic Party primary last spring unopposed, and in fact has not faced a serious challenge since the seat was created in 1971 and he was elected its first occupant.

But the very fact that no major figures have lined up to try to replace Fauntroy highlights an underlying problem: Many District politicians see the delegate's seat as a dead-end job. Fauntroy's situation is similar to that of comedian Rodney Dangerfield, who complains, "I don't get no respect." Fauntroy just phrases it more elegantly:

"I have to live constantly with what seems to me to be an obvious disrespect for what I do in this role as nonvoting delegate," he said in a recent interview. "This work is important, although it is not preceived by many to be that."

Once considered the most popular political figure in the District, Fauntroy now finds himself frustrated at not being closer to the actual running of the city. The limelight, power and patronage that come with responsibility for day-to-day governance is now monopolized, ironically, by officials in an elected city government whose semi-independent status Fauntroy helped fight for.

In addition, Fauntroy has failed to demonstrate much influence in affecting the course of the city's politics. He backed losing candidate Clifford Alexander for mayor in 1974 and Sterling Tucker for mayor in 1978, and this year supported his legislative aide, Johnny Barnes, in a losing campaign for nomination to the City Council from Ward 7. Fauntroy is the only major District political figure who opposes the statehood initiative on the Nove. 4 ballot, but said last week he believes it will pass over his objections.

Also, his career is closely linked to the now-stalled Voting Rights Amendment to the Constitution, which he shepherded through Congress. The amendment was passed in 1978, got off to a quick start and won approval in nine state legislatures. But approval of 29 more states is required, and the earlier momentum has now vanished.

The amendment would give the District two voting senators and at least one voting representative in Congress. Local observers have long speculated that if it ever receives final approval, Fauntroy would have the inside track for a Senate seat. But in the meantime, his political fortunes are, in effect, on hold.

Without acknowledging any linkage to his own career in politics, Fauntroy says he would like to stay on as non-voting delegate until a number of home rule measures are approved, including the amendment. He says he has no plans to run for mayor. "I want to do the job I set out to do," he said. "That is consistent with what I've been doing all my life."

He is opposed this year by two candidates -- Republican Robert Roehr, and Josephine Butler of the D.C. Statehood Party. Fauntroy is considered the favorite by a wide margin and has done almost no campaigning. In the months before the Democratic National Convention, he spent much of his time on the road touting, the presidential candidacy of Sen. Edward M. Kennedy, and since, he has been stumping through the South for President Carter,

Fauntroy, 47, began his involvement in politics in the early 1960s as an aide to the Rev. Martin Luther King Jr. with the Southern Christian Leadership Conference, working alongside young civil rights, activists like Jesse Jackson and Andrew Young.Young and Fauntroy were nicknamed the "Brooks Brothers" in those days because of their penchant for suits and ties at a time when most SCLC activists preferred bib overalls. Fauntroy planned logistics for some of the major SCLCerred bib overalls. Fauntroy planned logistics for some of the major SCLC-led civil rights demonstrations.

Fauntroy has never attained the same sustained national status as a Jackson or a Young, but he has made forays into national and even international politics. The latest such episode came last year after Young resigned as UN ambassador in the wake of a controversial meeting with a representative of the Palestine Liberation Organization. Fauntroy picked up the ball and met with PLO chief Yasser Arafat, explaianing that he was continuing the work Young began -- a move that alienated some Jewish voters.

Fauntroy today has a highly personalized view of his role over the years as a home rule advocate. He takes credit for a concept he calls "the arithmetic of power," the basic premise of which is that to secure home rule from Congress it is necessary to enlist the support of conservative Southern legislators, who can be persuaded to respond by black voters in their home states. This, he maintains, is how the Voting Rights Amendment made it through Congress.

"I always said we'd never be free in Washington until blacks could vote in the South," Fauntroy said. "Everybody laughed when I talked about the arithmetic of power. Hell, I went on and did it."