Brewster police chief Richard J. Koch Jr. said in a statement Monday that Oulton Hues, 73, of Norwood and Edgartown, and Robert Walker, 68, of Falmouth, were the victims who died in the single-engine plane crash in Cape Cod Bay on Sunday.

Mr. Hues was the pilot and a flight instructor; Mr. Walker was his student and co-owner of the plane, a Piper fixed-wing aircraft.

The plane left the Vineyard airport just after 9:30 a.m. Sunday. Mr. Hues, who was practicing flight holding patterns near Hyannis according to the Federal Aviation Administration, made contact with the air traffic controllers at 10:10 a.m. and reported smoke in the cabin. He then came back on and said the smoke had cleared. At 10:23 a.m. the FAA notified the Coast Guard that they lost contact with the aircraft.

The Coast Guard launched a search and rescue operation in the air and on the water that continued through the afternoon. State and local police and firefighters on Cape Cod also participated in the search.

In mid-afternoon Sunday the bodies of both men were recovered by Brewster fire department and the Coast Guard in an area called Saint’s Landing on the Lower Cape.

Brewster police said Monday that some pieces of the plane wreckage had been recovered from the icy waters of the bay.

FAA records show the plane was co-owned by Mr. Walker and Margaret M. Johnston of East Falmouth.

The cause of the crash remains under investigation.