New York's Democrat have created a runoff mayoral primay between two men who spent all summer competing for the same constituency - the white voters unprepared to give City Hall to Bella Abzug but eager to retire the incumbent, Mayor Abraham D. Beame.

The triumph of Rep. Edward I. Koch and N.Y. Secretary of State Mario Cuomo also was a victory for television advertising, which played a major role in making them known to voters who as late as July didn't recognize their names.

The constituency for Koch and Cuomo turned out to be just under 40 per cent of the vote, split almost evenly between them.

Thus in the 10 days before Democrats go back to the polls to narrow the Democratic field to one, Koch and Cuomo will be trying to sell themselves as the second choice to voters who preferred one of the five defeated candidates and to draw distinctions between themselves.

The telephones in losers' campaign headquarters were already ringing today as Cuomo and Koch solicited support.

Cuomo used his victory speech early this morning to lay some groundwork by praising each defeated candidate. He also said it pained him to be labeled by Koch as lacking in substance and he challenged Koch to a series of debates to see who is substantive and who is not.

Cuomo and Koch began the campaign being generally complimentary to each other in public and ended it exchanging barbs. Each hoped not to face the other in a runoff. Both calculated that Beame or Abzug would be easier to defeat because each had a hard-core of haters among the voters.

Cuomo, the only Italian-American Catholic in the race, accused Koch, who once had the reputation of being the classic Eastern liberal, of changing into conservatives clothing to suit the mood of the voters. Cuomo frustrated his advisers by refusing to move rightward in lockstep with Koch, but according to unofficial surveys he won an astonishing 82 per cent of the white Catholic vote.

For the first time in history, Cuomo campaign manager Michael Dowd had predicted, the white Catholic vote would be as big as the Jewish vote and he appears to have been right.

In the last few years, a candidate whose last name ends in a vowel has been assured of about 20 per cent of the vote citywide.

Koch, a liberal Jewish congressman who benefited in this campaign from being perceived as the most conservative challenger, split the Jewish vote with Abzug and Beame. Koch attacked Cuomo as indecisive and as a creature of Gov. Hugh L. Carey.

Cuomo had said publicly that he was not a candidate up to the time that Carey pressured him to run and then embarrassed him by making the first announcement of his change in heart. Cuomo counters allegations that he is Carey's puppet by pointing out that Koch had unsuccessfully sought Carey's support earlier.

While Cuomo's campaign appeared to be stumbling in early August, The New York Times rushed to endorse him. The New York Post and the Daily News followed with endorsements of Koch even though they had been leaning toward Cuomo in July.

Cuomo ran such a terrible campaign that they couldn't endorse him, Koch said.

Endorsements from losing candidates are likely to be shaped as much by personal grudges as by kinship by ideas.

Rep. Herman Badillo announced publicly that he will catch closely to see what Koch and Cuomo offer to the constituency of the poor he represents before making an endorsement.

Abzug is known to personally dislike Koch and therefore is thought more likely to endorse Cuomo [WORD ILLEGIBLE] is bad blood between Beame [WORD ILLEGIBLE] going back to New York's fiscal crisis and thus Beame is unlikely to endorse Cuomo, but Koch was one of Beame's sharpest critics this summer and he may choose to stay neutral.

Percy Sutton, the Manhattan Borough President, and the first black to run for Mayor, accused Koch of using code words to make oblique attacks on blacks during the campaign, but he is not close to Cuomo either.

For all of them there is the question how well they can deliver their vote if they try to. Municipal unions, most of which backed Beame, and, other groups also will be looking for new allianees.

For Koch and Cuomo, the problem will be how to maintain their posture as outsiders to the municipal power structure while gathering new supporters from within. Any such gathering will be done as quietly as possible.

Koch and Cuomo are certain to continue sparring about capital punishment. Koch favors it for heinous crimes. Cuomo opposes it and said this morning:

What we said in this campaign was that you can have law and justice . . . without being brutal and pandering to people's fear and without debasing yourself by taking positions that are too severe for any civilized society."

Capital punishment has become the symbol (the state, not the city, establishes criminal penalties) of the fear and prejudice of many New Yorkers. By supporting the death penalty, many people are expressing their desire for increased protection through the deterrent value they believe it has and for revenge on criminals."

The victory of Koch and Cuomo demonstrates that New York's economic bad times have not provoked a social protest by the poor. Rather, the fear of the poor seems a more politically potent emotion since the victors were the conservative candidates, if Beame, tarnished, by his record in office, is disregarded.

However, the results were extraordinarily close, with only 3 percentage points separating the top four finishers, in order, Koch, Cuomo, Beame and Abzug.

In addition, Sutton got 14 per cent and Badillo, who lost to Beame in 1973, won 11 per cent. If they had not divided the black and Hispanic-American vote, perhaps one of them would have been in the runoff.