EXCLUSIVE

Gail Zappa, the widow of music legend Frank Zappa has died. She was 70 years old.

The Zappa family tells TMZ ... Gail passed away Wednesday afternoon in Los Angeles. We're told she had been battling an illness for several years.

Frank and Gail married in 1967 and had 4 kids together -- Diva, Dweezil, Ahmet, and Moon.

The family says Gail "conducted intricate legal negotiations with corporations as grand dame of the Zappa Family Trust, she never failed to impart the sense of humor that was part and parcel of her indomitable and formidable personality."