Union spokesman John Melia says negotiations between the power company and Local 1-2 of the Utility Workers of America have been ongoing for 10 days.
The old contract expired at midnight and workers had threatened to strike, but talks continued early Sunday.
Con Ed spokesman Bob McGee says there are a wide range of issues being discussed from pensions to wages and health care. He says the company plans to call in managers to run the utility if there is a work stoppage.
The union represents about 8,500 workers.
The talks are occurring as New York braces for more hot weather. Many parts of the Northeast are under heat advisories or excessive heat warnings.
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