Jimmy Carl Black, who has died of cancer aged 70, was drummer and sometimes lead vocalist with Frank Zappa's Mothers of Invention between 1965 and the group's bitter break-up in 1970. The Mothers created concerts and albums that mixed pop-Dada, 1950s doo-wop, jazz, schmaltz, Stravinsky, Varèse and Webern. Black was to the fore as Lonesome Cowboy Burt, a highlight of Zappa's 200 Motels movie (1971). He was the man who introduced himself as "the Indian of the group" on the band's album, We're Only in It for the Money (1968), and was a central figure in If We'd All Been Living in California, a dialogue on corporate finances on Uncle Meat (1969).

Black, who inherited Cheyenne blood from his mother, was born in El Paso, Texas, but grew up in nearby Anthony on the New Mexican border. He was a soloist in his high school band's brass section, "but I realised that there was no chance in rock'n'roll for a trumpeter, after Elvis Presley appeared at El Paso Coliseum in 1955. When I saw the effect he had on those women, I thought, 'Man. That's what I want to do!'"

Though he could strum a guitar and had had piano lessons, Black bought a drum kit and practised by playing along mostly to black rhythm and blues records. While serving in the US air force, he joined a country and western trio, Them Three Guys, and, following demobilisation in 1958, played mainstream pop with the Surfs and then the Keys - with whom Black recorded Stretch Pants (1962).

Two years later, he moved to Los Angeles, and formed the Soul Giants, who played LA dance halls. When the guitarist was drafted into the army, he was replaced by Zappa, who told the band, according to Black, that "if you guys learn my music, I'll make you rich and famous".

"He took care of half of that promise," said Black, "because I'm damn sure I didn't get rich." Renamed the Mothers of Invention, the group followed Zappa's masterplan to a qualified prosperity via concerts and, later, albums. "Frank made me aware of modern classical stuff," said Black, "and very patiently taught me all those complex rhythms and time signatures."

But Black became increasingly unhappy about Zappa's control. He resented the enlistment of a second drummer, and Zappa claiming authorship of tracks such as If We'd All Been Living in California. "I never knew he'd taped it at a band meeting," he complained. "I wasn't credited. Everything was 'written, arranged and produced by Frank Zappa'. Then a week after a successful tour, he called us together and said, 'I've decided to break up the band. Your salaries have stopped as from last week.' It was a big shock. I had five kids to feed."

Postscripts to Black's tenure with Zappa embraced his role in 200 Motels, and an exhumation in 1981 of his character in it, Lonesome Cowboy Burt, for Harder Than Your Husband on Zappa's You Are What You Is album.

In 1972 Black had success with two albums as leader of Geronimo Black, named after his youngest son. But by 1974 a Melody Maker interview was conducted in Winebel's Donuts, where he was, indeed, making doughnuts.

He then moved to Albuquerque, New Mexico, released a solo album, Clearly Classic, which achieved minimal circulation, and joined a Captain Beefheart and his Magic Band world tour.

Black then settled in Austin, Texas, where he established the Gentlemen of Colour, a building-and-decorating business with Arthur Brown, the English star of the 1960s Crazy World of Arthur Brown. The firm flourished for 10 years - as did an artistic liaison which was to culminate in an album of R&B standards, Brown, Black and Blue (1980). Black was also performing with Eugene Chadbourne - "the free-est form guitar player I've ever met" - and the Grandmothers, initially, former Mothers band members fronted by the Italian guitarist and Frank Zappa lookalike Sandro Oliva. Their CDs included a concert recorded in 1998 at London's Astoria theatre.

Increasing success in Europe led Black to move to Vicenza, Italy with his then wife, a schoolteacher with the US army. After her death, he moved to Germany, home of his second wife Monika. In 1995 he began playing with the Muffin Men, the best British interpreters of the work of Zappa and Beefheart. Black was on the road with the group as recently as 2007. Assisted by Roddie Gilliard of the Muffin Men, he was working on an autobiography, For Mother's Sake.

He is survived by Monika, three sons and two daughters.

• James Carl Inkanish Black, drummer and singer, born February 1 1938; died November 1 2008