David Dinkins was a step away Wednesday from becoming New York City's first black mayor, having successfully used a healing theme to beat incumbent Edward Koch for the Democratic nomination. National Democrats, meanwhile, breathed easier after winning two House seats they had surrendered because of scandals.

Dinkins, the Manhattan borough president, combined extremely heavy black support with a healthy portion of the white vote Tuesday to easily capture the Democratic nod and stop the flamboyant Koch's bid for an unprecedented fourth term.Immediately, he struck the same chord that helped him stem a late Koch surge, telling supporters: "Remember me - I'm the guy that brings people together."

The Big Apple race was the hottest contest in a mini-Election Day that saw a handful of contests from coast to coast.

Key battles also included victories by Democrats Pete Geren in Texas and Gary Condit in California to capture the congressional seats once held by House Speaker Jim Wright and Rep. Tony Coelho - a pair of Democrats who resigned earlier this year because of ethics troubles.

In Detroit, incumbent Mayor Coleman Young easily placed first in that city's multi-candidate primary and will face accountant second-place finisher Tom Barrow in the November general election.

In New York, with all precincts counted, Dinkins had 537,313 votes, or 51 percent. Koch had 445,816 votes or 42 percent. Two other candidates picked up the remaining vote.

The win made Dinkins the first black to capture a major party's mayoral nomination and also established him as the clear favorite to win on Nov. 7, when he will face former U.S. Attorney Rudolph Giuliani.

He wasted little time playing the role of the conciliator, stressing his victory was broad-based and adding that the people "voted your hopes and not your fears."

For his part, Koch tried to encourage his disappointed backers, who realized they were watching the end of what has been one of the most unique mayoral administrations in the city's history.

"I want you not to feel sorry for me," Koch said. "Believe me, there is a life after the mayoralty."

Giuliani, known for his prosecutions of Wall Street and organized crime figures, easily defeated cosmetics magnate Ron Lauder in a GOP primary Tuesday. Giuliani had 67 percent of the vote to Lauder's 33 percent.

In past years the Democratic nominee was considered a sure winner, but this year the GOP has some hope Giuliani can reverse that trend.

Meanwhile, in Fort Worth, Texas, Geren defeated Republican Bob Lanier for the seat held for 34 years by the Wright, who was forced from office in June after a congressional ethics investigation of his finances.

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With all votes counted, Geren, a former aide to Sen. Lloyd Bentsen, D-Texas, had 51 percent, while Lanier, a doctor and television show host, had 49 percent. Geren's final margin was less than 2,000 votes.

In Fresno, Calif., meanwhile, Condit won Coelho's seat. With 91 percent of the vote counted, he had 57 percent. His nearest competitor in the seven-candidate field was Republican Clare Berryhill, who had nearly 35 percent.

Detroit's 71-year-old Young, seeking an unprecedented fifth term, had 50.7 percent of the vote while Barrow had 23.78 percent, beating out Rep. John Conyers, D-Mich., who had 17.7 percent. Young and Barrow will face each other in November.

Primaries also were held in a smattering of other cities, including Buffalo, N.Y., where three-term Mayor Jimmy Griffin, who already has Republican backing, added the Democratic endorsement for the November general election.

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