Newsday says they were discovered Sunday on separate stretches of East Hampton beaches.
The Riverhead Foundation for Marine Research and Preservation said they don't believe the two events are connected.
The first whale was found dead around 8 a.m. in Napeague. Officials say there were no outward signs of what may have caused the death of the 59-foot-long finback whale.
At around 2:30 p.m., officials got a report of a 5-foot-long juvenile pygmy sperm whale in nearby Amagansett. The foundation says it was euthanized because it had skin lesions and appeared "sickly."
Necropsies will be performed on both mammals on Monday.
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