But despite the high exposure, the Breckers stopped recording together in 1982. Now they're back, with an album - Return of the Brecker Brothers - and a series of concerts with a band of jazz-funk all-stars.
'We never intended to take so long a break,' says Mike, who at 43 is the younger by four years. 'We've been talking about it for years, but other opportunities got in the way.' Mike looks like a doctor and speaks like a Vice-Presidential candidate. His bearded brother blends into the background, occasionally muttering comments like an extra from a Cheech & Chong movie. They are jazz's answer to Was (Not Was).
In the 1970s these sons of a piano-playing lawyer were hot. They came from Philadelphia - the home of not only the Philly sound, but jazz stars such as Dizzy Gillespie, John Coltrane and Philly Joe Jones. Randy was first, hitting the New York jazz scene in the late 1960s. He landed gigs with the trumpeter Clark Terry and briefly joined Blood Sweat & Tears, who wedded rock with big-band jazz. Randy enjoyed playing with Blood Sweat & Tears, but wanted his own train set, and soon he had enlisted the help of his little brother.
In 1969 they formed the first of a series of influential fusion groups - Dreams. Featuring such luminaries as the drummer Billy Cobham and the guitarist John Abercrombie, they released two albums before splitting up. Randy and Mike found themselves courted by Horace Silver, James Taylor and Yoko Ono. Meanwhile they were making a fortune on the session circuit - appearing, credited and uncredited, on albums for Springsteen, James Brown, Joni Mitchell and Steely Dan among others.
'We did it partly for the money, partly for the experience,' says Mike, the voice of reason. 'We worked with a very high level of musicians and there were many things to be learned.'
'And it was short,' adds Randy. 'You went into the studio, they told you what to do and it was over in two or three hours.'
As session men, they found themselves at the whim of temperamental stars and producers. At one session with James Brown, the soul singer couldn't persuade the band of talented jazz musicians to play the funk he wanted, so he went to the drummer, Steve Gadd, and pulled him off the drum-kit. 'He started playing the drums himself, and he still couldn't get what he wanted,' remembers Randy.
For his part, Mike missed out on the chance to impersonate Clarence Clemons, the Big Man in Springsteen's band. When Clemons couldn't play a particular break, Mike was asked to fill in. 'I did it but they didn't like it so they asked David Sanborn, and he killed me. He played the break beautifully. But they didn't like that either and they cut it out of the record.'
Eventually the Breckers grew tired of being called in to add a few pa paas ('Ah, but what pa paas,' says Randy) and concentrated on their own group. In six barnstorming albums in the late 1970s, the Breckers made jazz-funk that lived up to its name - jazz that you could dance to.
When they moved on in 1982, it was Mike who came to prominence. Joining with Mike Manieri, he formed Steps Ahead (aka Steps, aka Five Easy Pieces). The band's name changed first because they were asked to do a Japanese tour, and the promoter could not pronounce Five Easy Pieces, and second because a North Carolina band called Steps threatened to sue.
Steps Ahead were a fusion fan's fusion band - they made the music you buy when you have graduated from Weather Report and Maze - and Mike soon found that he was hankering more towards acoustic jazz. A few sessions with artists on the ECM label, such as Kenny Wheeler, led him to his 1987 album, Mike Brecker, which won Down Beat magazine's Jazz Album of the Year award, and two follow-ups.
Last year was spent touring with Paul Simon on his Rhythm of the Saints tour. 'I've always been interested in African music and joining Paul Simon's band gave me the opportunity to play with and learn from African musicians.'
The African infusion can be heared on Return of the Brecker Brothers, particularly on the Cameroonian-influenced 'Wakaria (Wake Up)', as well as Brazilian lilts picked up by Randy from his wife, Elaine Elias. Mike rejects accusations of musical colonialism, levelled by such greats as Keith Jarrett, who regularly lectures his concert audiences on the evils of combining world music with jazz. 'It all depends on the intention of the musician,' says Mike. 'If a musican intends to learn, I don't think it applies.'
The Breckers do not intend to leave it 11 years before they record together again. 'We have it loosely planned to keep on making records every two or three years,' says Mike.
'That's unless other things get in the way,' adds Randy.
'It's a loose plan,' smiles Mike, ever the voice of reason.
The Breckers play the Royal Festival Hall on Wednesday 28 October. 'Return of the Brecker Brothers' is on GRP Records