With Washington making its traditional post-Labor Day return to business as usual, the campaign for mayor -- which smoldered like banked coals during the summer -- is expected to flare up.

When we left our saga, there was a large field of possible challengers to Mayor Marion Barry, who is expected to seek a second term. The list included former City Council chairman Sterling Tucker, Council Chairman Arrington L. Dixon, council members John L. Ray (D-At Large), Betty Ann Kane (D-At Large) and John A. Wilson (D-Ward 2), and two former Carter administration hands, former Secretary of Health and Human Services Patricia R. Harris and former Secretary of the Army Clifford L. Alexander.

The field, observers expect, will soon sort itself out and probably produce three or more serious candidates for next fall's Democratic primary -- including Barry. (As ever in District of Columbia politics, the Democratic primary is the election that really matters.)

But at this early stage, Barry's political strength is being debated.

"He may be the only one who's truly in the race at this point," said political consultant Douglas Bailey, whose campaign firm, Bailey, Deardourff and Associates, is handling council member Ray's campaign effort.

Yet, despite his incumbency, Barry's support is viewed by some observers as essentially soft. He squeaked through in the 1978 primary, and the observers believe his support has eroded, rather than expanded.

As for Barry's opponents, their chances of becoming serious candidates will depend on their ability to do certain things in the coming months.

Tucker, observers say, must find a way to capitalize on his strong name recognition among D.C. voters and convince them, in the words of a well-connected Washington lawyer, "that he's not Harold Stassen" -- whose name has become synonymous with the phrase "perennial candidate."n

Tucker was perceived as the man most likely to succeed former mayor Walter E. Washington in 1978, and the race was seen as his to lose. He lost.

"I think that any loss has to be overcome, there's no doubt about that," Tucker said recently. He added that he hopes to divert voters' attention to more positive images, and will stress his subsequent role in the Carter adminstration as an assistant secretary of Housing and Urban Development.

Ray is counting on developing a strong campaign organization to steal support from Barry, since the two men share much of the same political base. He recently announced the formation of an "exploratory committee" that included some prominent local citizens. But his problem is that many voters don't know who he is, and political pros are reluctant to back a candidate who is not known.

To help establish credibility, Ray hopes to raise $50,000 by the end of the year. Bailey and Deardourff are expected to have their tentative plan for the Ray campaign ready by then.

Wilson says that a draft committee promoting his candidacy already has nearly $40,000, and hopes to raise a total of $150,000 by the end of the year. He acknowledges that he, too, has a name recognition problem, as borne out in a recent poll. And Wilson may also have an image problem -- a reputation for unpredictability that has led some prominent players in local politics not to take him seriously when he says he wants to be mayor.

Wilson believes Barry starts with less than 30 percent of the vote and envisions a four-way race involving Barry, Tucker, Ray and himself.

Kane is the only white in the field of prospective candidates, and an official of a respected polling firm suggested recently that she should do everything she can in the next few months to encourage a large field of candidates -- including deliberately not raising so much money that potential candidates would be scared off.

A large field, the reasoning goes, would splinter the black vote and make it easier for Kane to win. Kane maintains that race need not be an issue in the election. A number of former supporters, however, have tried to discourage her from running, and Kane now speaks more often than in the past of running for council chairman.

Dixon, who has flirted with the idea of running for mayor, faces two choices and must make a decision soon, observers say. He could run for mayor, but he is believed to share much of Tucker's black middle-class constituency and the two might neutralize each other.

Dixon also could run again for council chairman but one or two candidates who eventually drop out of the mayor's race may take him on. Kane, Ray, Wilson and council members David A. Clarke (D-Ward 1)and Charlene Drew Jarvis (D-Ward 4 ) all could end up in the chairman's race against Dixon, under the right circumstances.

Harris and Alexander have their backers, and neither has the name recognition problems of some of the council members. But aside from cocktail party chatter about the possibility of their running, neither has done much to set up a campaign organization. They will have to do so before the end of the year if they are serious.

It should be, in fact, an interesting few months as speculation gives way to political combat.