The race for chairman of the D.C. City Council heads into its final two weeks with the three candidates locked into a grueling neck-and-neck struggle in which images appear to have become just as important as issues.

Incumbent Arrington Dixon is trying to stave off the twin challenges of former chairman and veteran D.C. politician Sterling Tucker and Ward 1 Council member David A. Clarke, who is no longer considered the long-shot candidate suggested by early polls.

"David has made some very significant strides," said one influential businessman who is supporting Dixon. "The perception had been that Tucker's entry in June would make it a two-person race between Tucker and Dixon. I think David for the first time has established a citywide organization."

So far, despite some differences on issues and contrasting campaign tactics, none of the candidates has emerged as a clear favorite in the race for the second highest elective office in city government.

"I think it is a good horse race, probably pretty close with everybody still in it," said Tucker.

There is no provision for a runoff after the Sept. 14 Democratic primary and there is no Republican or independent to face in November.

At times, the debate among the candidates becomes dizzying as all three reach back over more than eight years of legislative and intramural political battles.

There are conflicting claims of who was first to introduce a bill or amendment and who opposed or ignored a certain issue, leaving those less knowledgeable swirling in three diferent versions of council history.

For example, during a candidate forum and call-in program broadcast yesterday on WHUR-FM, Dixon noted that the Council under his leadership funded the city's new convention center, which is supposed to provide thousands of jobs. That prompted Tucker to point out that the center was initially approved while he was chairman.

Although he didn't have an opportunity to do it yesterday, Clarke usually chimes in that center proposal came from neither Dixon nor Tucker, but former mayor Walter E. Washington.

As a result of such verbal sparring, images have become increasingly important, political observers say, as the candidates turn toward the closing days of the campaign.

Tucker, 58, is stressing his role as the first chairman of the elected Council from 1975-78, telling voters that he was viewed as a seasoned and moderate leader who could hold the 13-member legislature together. He says under Dixon "the council has lost its way."

Tucker ran unsuccessfuly for mayor in 1978 and got into the chairman's race late this year after a second bid for mayor foundered. Now he is trying to raise funds for a media blitz to capitalize on his name recognition, which remains high. He has begun running radio ads and has taped a television commercial, although an aide said he does not yet have the funds to air it.

Dixon, who was elected chairman in 1978 after serving four years as the Council member from Ward 4 in upper Northwest, is emphasizing his life-long career in Washington and his rise from a ward-level council member to chairman. "I am a symbol for the youth of this city," Dixon, 39, says at forums, adding that he is "the candidate of the future, not the past" -- a shot at Tucker.

"We are going to continue to emphasize the positive aspects of the chairman and reinforce the message that he has served the city well and deserves to be reelected," said James Christian, a Washington lawyer and Dixon adviser.

Dixon has sent out urgent fund raising appeals in hopes of putting on his own media blitz. He also is concentrating on an elaborate election-day transportation network to make sure targeted voters get to the polls.

Clarke, 38, has nurtured a reputation as one of the most issue-oriented members of the council. Like Tucker, he also has a history of work in civil rights movement and the fight for home rule in Washington.

Clarke has relied heavily on that image in his chairman's race, suggesting to voters that he will bring a new sense of activism to the chairman's job that he says has been missing under Tucker and Dixon. Some radio ads promoting Clarke have already begun, others are expected this week and Clarke says he has not ruled out television ads.

Clarke has put together a large list of endorsements from organized labor, preservationists, tenants, women, gay rights supporters and several political organizations.

"My campaign has addressed itself to an appeal to ideas, people who believe this or that should vote for me. Now, I'm going to have to pull that in" on election day, Clarke said.

While there are three candidates in the race, many political observers believe that two general constituencies are being sought.

In many respects, Dixon and Tucker are seen appealing to one group of largely middle-class, church-going voters who live in the city's outer ring of predominantly-black neighborhoods of Wards 4, 5, parts of 6 and 7 that accounted for about 50 per cent of the 89,042 votes cast in the 1978 Democratic primary for chairman.

Both Dixon and Tucker have targeted much of their campaigns to those high-voting precincts and some political observers feel they could neutralize each other.

That could permit Clarke to win on the strength of his acknowledged base in Ward 1, the city's only melting pot ward, and pockets of organized support concentrated in affluent and overwhelmingly white Ward 3 west of Rock Creek Park, Wards 2 and 6 in the inner city and parts of Ward 7 and 8 in far Northeast and Southeast.

That scenario could have an unsettling ring for Tucker, because it is a virtual replay of the 1978 mayoral primary which he narrowly lost to Marion Barry.

In that race, Tucker and former mayor Walter E. Washington split the same essential constituency that Dixon and Tucker are competing for now, allowing Barry to put together a winning coalition very similar to that now being targeted by Clarke.

Clarke, however, has tended to downplay his expected support in Ward 3 in an effort to avoid any hint of racial politics. He rarely mentions the ward when discussing his strategy, and his endorsements include the backing of several key influential blacks and black-oriented organizations.

Tucker says history will not repeat itself because he also expects to win votes from poor areas and labor union members whose leaders have endorsed Clarke.

Dixon has raised the most money, reporting receipts of about $150,000 in the required Aug. 10 finanical filing, far below the $350,000 he had hoped to raise. Ruth McClain, Dixon's campaign manager and one of his chief strategists, said last week, "We see media as an important part. It is not as ambitious as our original projection. Clearly we are behind that, therefore our media will reflect the changes in our income."

Tucker, who reported raising $50,000 as of Aug. 10, is trying to shake the image of an ineffective campaigner that hurt him in his mayor's race in 1978. At recent forums, Tucker has purposely walked toward audiences to avoid being called "standoffish" and has tried to deliver stronger speeches.

"I'm much more aggressive in my handshaking and speaking. There is a change in Sterling Tucker's campaign style. I find my audiences responding to it. I feel up and I'm not a reluctant candidate," Tucker said last week.

Tucker said his main campaign problems continue to be a lack of knowledge among voters that he is running for chairman again and questions about whether he doesn't really want to be mayor. "People don't wonder whether I'm qualified, people wonder do I want this job. I do, I believe I can make a difference."

Tucker's own election day plans are muted because of his late start after toying with the idea of running at-large. "As far as a real get out the vote effort , we don't have the time," one Tucker campaign strategist said.

Tucker's late entry into the campaign also cost him some support. The political action arm of the Greater Washington Board of Trade has endorsed Dixon, for example, although business leaders said Tucker will get some money from business groups. "There is some nostalgia for Sterling," said one business official. But "his timing and way of entering into the race blocked him out of it."

On the stump, Tucker generally sticks to a campaign theme that the chairman of the council can help improve housing in the city, promote job opportunities and the overall quality of life.

He has sought to separate himself from Clarke and Dixon by opposing other bills passed or pending in the Council under Dixon's leadership. They include measures that led to reductions in benefits paid out under workers compensation and unemployment programs, expansion of the city's minority contracting law to include Pacific and Asian Americans and Hispanics of European descent.

Dixon boasts that under his leadership the Council acted on controversial issues that were never addressed during Tucker's four years as chairman -- especially no-fault insurance and cable television.

He also claims credit for increased funding for public schools and cites his role as one of the leaders who helped defeat an educational tax credit initiative rejected by voters last year.

Dixon yesterday claimed credit for leading city government efforts to stave off the effects of Reagan administration budget cuts. But Clarke took Dixon to task on those claims, saying that Dixon had voted against increased Medicaid funding for city residents.

Clarke, who reported raising about $70,000, has emphasized his longtime support of rent control and his opposition to widescale conversion of apartment buildings to condominiums -- stands that he says he would continue as chairman.

That was in keeping with a general theme of the Clarke campaign -- that the same stances he has taken on various issues of housing and criminal justices issues as a Ward 1 legislator would be his if he is elected chairman.