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Cindy Williams, an actress best known for her role in the popular 1970s sitcom Laverne & Shirley, has died at the age of 75, her family said.

Williams had a long show business career, also appearing in movies including George Lucas's 1973 film American Graffiti.

She died peacefully last week after a brief illness, according to the statement from her children.

Emily and Zak Hudson called their mother "kind and hilarious".

Her death "has brought us insurmountable sadness that could never truly be expressed", they said in a statement on Monday that was shared by family spokesperson Liza Cranis.

"Knowing and loving her has been our joy and privilege. She was one of a kind, beautiful, generous and possessed a brilliant sense of humour and a glittering spirit that everyone loved."

Her two children said their mother was dedicated to rescuing animals, her faith, and making the world laugh.

In Laverne & Shirley, Williams starred opposite Penny Marshall - who played Laverne DeFazio - as two single working women in Milwaukee, Wisconsin in the 1950s. The sitcom ran on ABC from 1976 to 1983.

The show was among the most popular on TV at the time and earned Williams a Golden Globe nomination for best actress in a TV series for her portrayal of the cheerful Shirley Feeney.

Williams was born in the Van Nuys area of Los Angeles, California in 1947.

She had film and TV credits spanning decades, including appearances in Happy Days as Shirley Feeney and in director Francis Ford Coppola's 1974 movie The Conversation.