The New York Times said the cause of Adamson's death was unknown as of Wednesday.
The Cocteau company was launched in a converted Greenwich Village storefront in 1971 by Adamson and a group of her fellow actors. The troupe performed a variety of classic plays that won plaudits from critics and soon became a keystone of New York's Off Broadway scene.
In 1981, Adamson directed "Something Cloudy, Something Clear," the last play written by Tennessee Williams to premier in New York while he was still alive.
Adamson, a native of Beverly Hills, stepped down as artistic director in 1989 after 18 years on the job but quickly became active in the Phoenix Theatre Ensemble, which was formed by Cocteau alumni.