City politicians have been complaining privately ever since D.C. Del. Walter E. Fauntroy began urging the candicacy of Sterling Tucker for mayor in this year's election. Their problem is not so much with his choice as with his assertion that there is a political hierarchy in which Tucker has earned the right to be the next mayor. Some think Fauntroy is trying to become 'Boss Walter.'

Fauntroy feels that without an orderly process of picking mayoral candidates there will be a split in the ranks of the party's regular Democratic organization that could render it ineffective. His critics contend that in an overwhelmingly Democratic city, such a division is not only inevitable but undoubtedly necessary if the Democratic Party is going to remain democratic and if the voters are to be given an open choice during the primary election.

Indeed, even among some of those closest to Fauntroy, there is a private admission that the very tactics being used by Fauntroy as he pushes the mayoral candidacy of City Council Chairman Tucker could become an issue in the election.

Councilman John A. Wilson (D-2), who knows a lot of the ins and outs of city politics and has established a reputation as a knowledgeable political operative, takes a dim view of all this. During the more harmonious days of 1971, Wilson managed Fauntroy's first congressional campaing. But now he says he's afraid that if things keep going the way they are, not only will the city's regular Democrats be in deep disarray, but city government will be in so much chaos that Congress may be discouraged from authorizing any expansion of the city's presently limited form of home rule.

"The way it is now, we're going to end up with Walter Washington as mayor, Doug Moore as chairman of the Council, Sterling Tucker and Marion Barry unemployed and two of our best people out of the picture and out of the government," Wilson said as he sat in his city hall office the other day.

"If Walter Fauntroy wants a change, he should come down off the Hill and run against Walter Washington (for mayor). He should leave the 100-yard dash up there and come down here and run the mile in the mess with the rest of us.

"That way you would have 'Big Walter' (Washington) against 'Little Walter' (Fauntroy) and the people could decide if they really want change. If 'Little Walter' wins, the people want change. If 'Big Walter' wins, the people don't want change."

One thing Wilson talks about that few others discuss is the fact that the potential cast of characters for this fall's political drama could bring about a turnover of 10 of the 14 elected positions in city hall. Already the mayor's office and seven Council seats, including that of the chairman, are up for grabs. But if Marion Barry leaves his at-large seat to run for mayor, as expected, and Arrington Dixon vacates his 4th ward Council seat to run for chairman, nine of the Council's 13 seats would be open in a single election year. That, Wilson feels, would lead to chaos.

One belief Wilson shares with Fauntroy - and probably most other Council members as well - is that Tucker has developed into a good Council chairman. But precisely for that reason, Wilson argues, Tucker should remain on the job for another four years, rather than let someone else go through on-the-job-training at a time when the city is pushing for expansion of home rule.

Wilson also agrees with Fauntroy that the city's regular Democrats, who united behind Barry, Tucker and Fauntroy in 1976 to seize control of the party organization, are sharply split over the rival candidacies of Barry and Tucker. But Wilson believes the divisions will result in a split that will propel Washington to reelection, while Fauntroy thinks he can still usher through a victory by Tuckery.

"It will be a fantastic squeeze play if it's pulled off, but it won't bring about no change," Wilson said, contending he is not in a pitched political battle with Fauntroy. "Nobody's going to win by enough plurality to give them a united party or any base of strength."

For these and other reasons, Wilson says he has decided that he will endorse no one for either mayor or Council chairman, and probably not work in anyone's campaign.

Wilson says his efforts will be aimed at convincing Fauntroy to run for mayor against Washington, with Tucker as the candidate for chairman and Barry not running for anything. Barring that, Wilson said, he thinks everyone should remain where they are,

During his appearance at Monday's program honoring Martin Luther King Jr., comedian and human rights activiquently been asked if it had been difficult during the non-violent civil rights marches.

"They had some big white Mississippi sheriffs," Gregory said, "and when you looked at them that's all the restraint you needed."