John B. Hynes was reelected for his third term in office as mayor of Boston in one of the many nationwide local elections yesterday.

In a victory speech, after State Senator John E. Powers had conceded defeat, Hynes predicted an "economic rebirth" for the city during the coming administration."

At 11 p.m. last night, with 260 of Boston's 200 precincts counted, Hynes was reported about 13,000 votes ahead of his opponent. Two hours earlier, Powers had 51,000 votes over Hynes's 50,000, at which time 120 districts had been heard from.

After Powers' concession, Hynes made two speeches, one in his Milk St. headquarters and one in the Sheraton-Plaza. A campaign worker estimated that a "noisy" crowd of about 400 people heard the mayor speak. "Why shouldn't everybody rejoice?" she commented. "Mayor Hynes won the election."

In his speech at the hotel, Hynes said, "I am of the opinion that Boston is on the verge of a great business revival. I hope to help and speed the economic rebirth of our city." He said he "was thankful to all those who have voted for me."

Powers Congratulates Hynes

At the same time, Powers congratulated the mayor and expressed the hope "he will have an abundance of good health to carry on the prosecution of his office."

Because of the proportional representation type of voting done in Cambridge, there will be no results in the races for the City Council and the School Committee before tonight, according to Russell Peck, publicity director of the Cambridge Civic Association. Even if the counters work until midnight, Peck said, the unofficial results cannot be anticipated until Wednesday night.

Under the system of proportional representation, voters choose from among the 41 Council and 19 School Committee candidates by numerical preference. The counters will have to go over the ballots 41 times, Peck explained, before all the unsuccessful candidates are eliminated.

In most of the city elections throughout the country, Democrats were gaining the ascendancy.