Although still a year remains before the 1978 campaign, some of Washington's better-known Democrats have already begun jostling in earnest for the party's mayoral nomination.

City Council member John A. Wilson (D-2) let the word float out last week that he is available for the job. "If it's going to be a free-for-all," Wilson said, "my chances are going to be as good as anybody else's."

Wilson's Council colleague, Marion Barry (D-at large), widely believed to be a possible mayoral contender, lately has acquired a spruced up wardrobe, and has been making frequent visits to various community agencies and issuing a flurry of press releases, some of which are implicitly critical of a major rival for the nomination, Council Chairman Sterling Tucker.

Recently for example, after Tucker urged Virginia Gov. Mills E. Godwin to put up or shut up on his announced plans to release $36 million in state funds for the Metro system, Barry introduced a council resolution implicitly aimed at embarrassing Tucker.

Barry's resolution would force city representatives on the Metro board --including Tucker -- to oppose a proposed Metrobus fare increase. Tucker has been in favor of the increase in Metrobus fares.

Tucker says he has not yet made up his mind whether he will run for mayor, even though many city political observers consider him the early front runner.

Mayor Walter E. Washington is insisting, meanwhile, that he should not be expected not to seek a second elected term, although he would have to run on record as elected mayor who was plagued with allegations of mismanagement, nepotism and cronyism.

Democrats make up the vast majority of the city's electorate, so that winning that party's mayoral primary is likely to be tantamount to victory.

Supporters of both Tucker and Barry -- who are the most frequently discussed mayoral possibilities -- agree that in the current political situation Del. Walter E. Fauntroy (D-D.C.) holds the trump card because he has been the most effective vote getter in the city. Last fall, in his fourth successful race for D.C. delegate, Fountroy racked up 77.7 per cent of the vote.

In 1974, Fauntroy's 11th-hour backing of lawyer Clifford Alexander failed to stop Washington. However, with two or more candidates of more equal strength in the field -- such as Barry and Tucker -- a boost from Fauntroy could mean the margin of victory, observers believe.

Another factor in the political infighting is the Council chairmanship that, in the view of some, frequently rivals the mayor's office in prestige, public exposure and power. As Tucker has shown during the past two years, the post can be a logical launching pad for a mayoral campaign. It could also be a tempting concession one mayoral candidate could offer to a potentially menacing foe.

According to several District Building sources, some of Tucker's supporters hope Barry will decide to run for Council chairman instead of opposing Tucker for mayor. If that were done, these sources say, the city's Democratic party could avoid a potentially bitter contest for the mayoral nomination and field a Fauntroy-Tucker-Barry slate that would probably be unbeatable.

Many city Democrats -- including central committee chairman Robert B. Washington, Jr. -- are reluctant to discuss the mayoral race publicly, contending that it is still too early to tell what's going on. However, several leading city Democrats offered this scenario.

Tucker, 53, whose term expires in 1978, will run for mayor or nothing at all. He is the favorite candidate among city businessmen, who see him as the person who has held a sometimes unpredictable City Council "in check." Said one promient city Democrat, "if nothing comes out bad about Sterling Tucker, if his shirts are all clean, he's got it made."

One liability for Tucker, however, could be his close association of the past with Mayor Washington, with whom he ran in 1974. Since then, however. Tucker has tried to place considerable distance between himself and the mayor's administration and was one of the leaders of a united Democratic coalition that last May defeated Mayor Washington's forces in a battle for control of the party's central committee.

Of all the early hopefuls, party insiders said, Tucker is most likely to get Fauntroy's support, because of long-standing friendship between the two. Shoring up that support will be a key factor in Tucker's decision to run for mayor, the sources said.

Barry made a conscious effort four years ago to broaden his base by becoming chairman of the Council's finance and revenue committee, whose actions are closely monitored by the city's business community. Barry, a militant civil rights activist in the '60s, has dispelled some of the distrust among businessmen, but Tucker enjoys greater support from them.

Barry, 41, got almost as large a proportion of the vote as Fauntroy did in last year's election, and would be a strong contender for the Council chairmanship. Putting his larger political aspirations on the back burner for four or eight years to avoid a head-on fight with Tucker for mayor, could be risky or even fatal to his career.

Some of Tucker's supporters believe that Barry will have to decide quickly on what he wants to do in order to prevent lesser known Democrats --such as Council member Arrington Dixon -- from getting an early jump in the race for chairmanship and eroding some of Barry's support.

Mayor Washington is 61 and many observers believe his election in 1974 was in part a show of appreciation for his past service as appointed mayor since 1968.

Since being elected, however, the mayor's administration has been burdened by accusations of mismanagement in the human resources, environmental services and finance and revenue departments.

"I think he's out for '78," said a ranking party official who backed the mayor in 1974. "There's going to be so much thrown out about mismanagement and (suspended DHR director) Joe Yeldell that I don't think the mayor could stand the fire."

Fauntroy and Tucker, along with none other Democrats on the City Council, resoundingly defeated the mayor's open party slate in the May contest for control of the Democratic central committee in party by running on a platform that labeled the mayor's administration wasteful and inefficient.

Douglas E. Moore (D-at large) one of the mayor's strongest supporters in the Council, has said that he will run for mayor in 1978 if Washington does not. Moore, the former head of the Black United Front, got more votes than other at-large candidates in the 1974 election.

In this year's Council reorganization session, Moore was stripped of the chairmanship of the powerful budget committee. The actions against Moore stemmed from his involvement in two widely publized personel disputes and from his performance as head of the vital Council committee. Moore says if he does not run for mayor be will run for Council chairman.

Wilson, whose ward includes much of the downtown area, insists that he is a serious mayoral candidate. "I think I could handle the job and I'd like to have the job," he said. "I think I've got more vision of what could be done to the city and for the city than the things I've heard in the past."

Some sources believe Wilson could be a stalking horse for his long-time friend Barry, and might support Barry in exchange for some favored political treatment.

Other names being mentioned as possible mayoral candidates are Dixon, retired Superior Court judge Harry T. Alexander, former city Bicentennial director Knighton Stanley and H. R. Crawford, who was an assistant secretary of Housing and Urban Development in the Nixon Administration.

All of the most talked-about candidates are in the current city government. "They'd have a particularly hard time running if someone was accusing the city of mismanagement because they would be seen as part of the problem," one city Democrat said.

Some people are really looking for a new face in city politics, one businessman said. "but right now, no one has the slightest idea who that could be."