The most intense campaign in town at the moment may be, not for mayor, but for the opportunity to be a judge of the D.C. Superior Court. Six well-mannered candidates are in a behind-closed-doors race for what amounts to a prestigious job that usually lasts a lifetime and pays more than $60,000 a year.

The mayor's race is fought pretty much in the open. It is a campaign in which candidates are judged by an electorate of thousands. Money must be raised, issues debated, organizations developed and put to work. The campaign for a judgeship is of a different nature, however. It involves private phone calls, private letters, inside connections and old friendships.

And the six candidates vying to replace two retired Superior Court judges--William E. Stewart Jr. and Dyer J. Taylor--are pushing every button and pulling every lever. The candidates are Francis D. Carter, head of the Public Defender Service; Matthew S. Watson, former city auditor now in private practice; Bruce Beaudin, head of the D.C. Pretrial Services Agency, and private attorneys George Mitchell, Steffen W. Graae and Patricia Wynn. Wynn and Watson are in the same law firm, Stiller Schwartz, Kaswell & Perazick.

"With Reagan in the White House," says one of the candidates, "the process is more political this year than it's ever been. It was political under Carter, but now you have to get past a liberal, Democratic selection panel on the local level and then a conservative, Republican White House. No virgins are going to come out of this."

In most states the process of selecting a judge would be openly political. Candidates seek the support of the party in power to get appointed to the bench. In the District, there is an ostensibly less political procedure involving the D.C. Judicial Nomination Commission, whose members are appointed to terms by diverse elements such as the mayor, the U.S. District Court and the D.C. Bar. For each judicial position the commission recommends three candidates to the White House, and the president nominates one of the three for Senate confirmation.

The campaigning starts with the commission. "If someone is considering you for a position," says candidate Francis Carter, "you do your best to find out their (commission members') background. It's nothing underhanded. You aren't necessarily going to play to them individually, but it will be helpful when you meet with the commission and they start asking questions.

"If you know who they are you can guess what kind of questions they are going to ask. . . . You want to know if they work in the government or private practice, how long they've lived in the city, who their friends are."

It is also necessary to calculate the political connections of the commission, the candidates say. Lawyer Charles T. Duncan, who was D.C. corporation counsel under Walter E. Washington, the District's first mayor, is now treasurer of Patricia Roberts Harris' mayoral campaign. Businessman John W. Hechinger Jr. is a key fund-raiser for Mayor Marion Barry and believed by some to be close to U.S. District Judge Harold H. Greene, another member of the commission.

The current head of the commission, lawyer Frederic B. Abramson, served on Barry's 1978 transition team. Labor leader William Lucy, another commission member, has many of his roots in the old Walter Washington camp as well, but also is a good friend of the chief judge of the D.C. Court of Appeals, Theodore R. Newman.

Just as important as impressing the commission, however, is making an impression on the White House. Every candidate for the current court openings is aware that one of the recent winners was Ronald P. Wertheim. In 1975 Wertheim successfully represented former assistant attorney general Robert C. Mardian in the Watergate conspiracy trial. Fielding was assistant counsel to then-White House counsel John Dean. Fielding disqualified himself from Wertheim's selection, but since then candidates for judgeships have become even more impressed with the importance of having a friend in the White House.

"In the White House, we tried to talk to people who knew the candidates," says Douglas Huron, who was an assistant counsel to President Carter. "We also tried to talk to people who were active in the city--particularly lawyers."

The talk of the town can mean as much as a candidate's record.

"It's good to get someone on your side who's got the connections in the White House or the commission," says candidate Steffen Graae. "I'd imagine everyone is looking to see who they know who may know Fielding, or someone on the commission."

Then there is the question of the Senate. Will a Republican senator's call influence the White House?

"The way I look at it," says candidate Matthew S. Watson, the former D.C. auditor, "you can't be overly aggressive. I've had people write letters of recommendation for me. I want to get out my credentials as a crusader for efficiency in government, a fraud fighter, to impress Reagan's people."

In addition to the two openings on the Superior Court, there is one vacancy on the D.C. Court of Appeals. The candidates for that judgeship are Sylvia Bacon, a Superior Court judge and a Republican who was appointed to the court by President Nixon before there was a Judical Nominations Commission; J. William Doolittle, an attorney who is a Democrat; and John A. Terry, an assistant U.S. attorney in the Justice Department who states no political affiliation. The White House has until May 7 to choose a nominee for the appeals court judgeship, and until May 20 to decide who will fill the Superior Court seat, but the announcements could come at any time.

Last week, Mayor Barry took a potshot at challenger Patricia Roberts Harris by having his supporters organize a fund-raiser and fashion show with the members of Harris' sorority, Delta Sigma Theta.

The event was held Thursday night at the home of Priscilla Adkins, wife of developer James Adkins, and about 70 Deltas attended the $25-a-person affair, including Barry's wife Effi, his budget director Gladys Mack, School Board member Linda Cropp and D.C. Council member Hilda Mason.

The talk in the crowd was that Harris, former Delta executive director, had not paid her Delta dues until she began thinking about running for mayor. Not so, responds Harris.

"That's none of their business," she said. "But I have been, and yes, I am paid up . But it's none of their business because none of them is a member of Delta Sigma Theta; . . . even if their wives are members, it's none of their business. . . . This petty, small-town gossip is what people are tired of."