After a two-week delay in their primary elections, New Yorkers will go to the polls Tuesday with Mayor Edward Koch, endorsed by both Republicans and Democrats for the first time in the city, considered an easy winner.

His opponents, none of whom has ever been regarded as presenting a serious challenge, include Democrat Melvin Klenetsky, a schoolteacher who once ran for Illinois governor on the U.S. Labor Party ticket; Republican John Esposito, a city Assemblyman whose major campaign expenditure has been a $210 campaign song, and Democratic Assemblyman Frank J. Barbaro, the most serious rival, who attacked Koch for being "pro-landlord" and insensitive to minorities.

Two days before the election, however, Barbaro, while insisting he can win, told reporters that "if Koch doesn't win with at least 75 percent of the vote, it will be a disaster for him."

"I guess he's conceded already," Koch said.

Koch, a tremendously popular politician who is his own best cheerleader ("I could always get a better job, but New York couldn't get a better mayor"), has made no secret of his desire to be a three-term man. He has based much of his campaign on the claim that he restored the city to fiscal health and that, while many services were of necessity reduced, he is about to increase services again. Still, even with the feeling here, since the beginning of the year, that he was unbeatable for a second term, Koch has campaigned hard.

He has spent over $1 million, according to his campaign consultant, Maureen Connelly. The reason, according to Connelly, a partner in the Dave Garth firm of Garth, Maiorana, and Connelly, is that the mayor "doesn't take anything for granted."

Local political observers concur, but suggest another reason. The mayor retained the Garth firm, and retained it early in the game, they say, to prevent anyone else from doing so.

That desire to win, however, hasn't inhibited the mayor--known to his detractors as "Mayor Mouth"--from campaigning in his usual outspoken style. Faced this past Friday with a Brooklynite who criticized the city's dirty streets (Brooklynites are as legendary as Koch when it comes to lack of inhibition), Koch replied with a raised middle finger. Later, he blithely dismissed the gesture as "a three-fingered Boy Scout salute."

Originally scheduled for Sept. 10, the New York City primary elections were canceled hours before the polls were to open when a federal court ruled that New York had violated the Voting Rights Act in drawing up new City Council boundary lines. The suit had been brought by black and Hispanic groups.

Races for the majority of the City Council seats have now been indefinitely postponed. Nonetheless, major local races, including those for city comptroller, Manhattan borough president, and Brooklyn and Queens district attorneys will be held.

Of those races, one of the most heated is for the office of Brooklyn district attorney, with former congresswoman Elizabeth Holtzman, who lost in a bid for a Senate seat last year, opposing Norman Rosen, who for 12 years has been the executive assistant district attorney under Eugene Gold.

Nationally known as the tough young "prosecutor" who grilled Nixon during the Watergate years, Holtzman lost in her Senate race when Sen. Jacob K. Javits, rejected on the Republican line, ran as a Liberal, dividing the liberal vote between Holtzman and himself, and enabling dark horse Alfonse D'Amato, a conservative Republican, to capture the seat.

Holtzman has since been teaching full time at New York University. Some critics contend that her bid for the office is merely a way to keep her name politically alive--a feeling that Mayor Koch, who has been cool to Holtzman for some time, voiced early this week, after an 11th-hour endorsement of her opponent.

"Liz Holtzman does not have enough experience in my opinion and she doesn't even want the job," the Mayor told The New York Times.

Some political observers assert, however, that neither Holtzman, who has received the powerful Times endorsement, nor her opponent, who is backed by the Brooklyn Democratic organization, is truly qualified for the job.

Rosen's duties, as an executive assistant, had little to do with overseeing cases. Holtzman, though she stresses her efforts to punish Nazi war criminals and her "workhorse" record in Congress, has no experience as a prosecutor.