Kofman says her husband went in for surgery on a clogged artery in one of his legs.
The surgery was successful, but he later developed pneumonia; he had been in critical but stable condition for about a week.
Welch was elected mayor in 1994 after four years as a borough councilman.
He was born in Philadelphia but lived most of his life in State College.
He graduated from Penn State University in 1964 and later worked at the Centre Daily Times newspaper.
In addition to his wife, Welch is survived by three daughters, two granddaughters, three brothers and a sister.
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