They are a family orchestra from a mysterious small town called Szegerely in the Balkans, got spotted by the Globestyle Music while playing at a National Refrigeration Conference Dance, and were smuggled out to Britain with a help of their Uncle Patrel. So the story was told, and they became a cult band in the world of World Music touring countries including the US, Canada, Japan, and even Bulgaria!
The Mustaphas had their debut gig in London on 6 August 1982, and released a mini album "Bam! Mustapha Plays Stereo" in 1985. The original line-up of the band was Hijaz Mustapha (bouzouki, violin, Hawaiian guitar), Houzam Mustapha (ds), Isfa'ani Mustapha (percussion), Oussack Mustapha (cello), Niaveti Mustapha (accordion, flute), and Uncle Patrel (saz).
According to an interview of Ben Mandelson (aka Hijaz), it was Tim Fienburgh (= Niaveti) who came up with an idea of doing 'some kind of weird Balkan wedding band thing'. Colin, who played in Orchestra Jazira together with Ben (= Hijaz) and Nigel Watson (= Houzam), joined the band in mid-1985 replacing Oussack, acquired the name Sabah Habas Mustapha, and played a role of the younger brother. In his interview (as Sabah Habas) in "Folk Roots", No. 182/3 (Aug./Sep. 1998), Colin says, after Oussack was kidnapped by the Oyster Band, he got kidnapped into 3 Mustaphas 3 despite his protest that he didn't play cello and only played electric bass ;-)
By the time 3 Mustaphas 3 released their first full album "Shopping" in 1987, Kemo Mustapha (accordion, key) had joined the band, and later Daoudi Mustapha (woodwinds) was added. Other "family" members such as Expen$ive Mustapha (trumpet) and Lavra Tima Daviz Mustapha (vo) appeared from time to time.
It is said that the initial idea was doing a band where they could do all the crazy things, but at the same time they studied different types of music from various parts of the world, and blended them into their own eclectic music. They also worked for various musicians, including Ofra Haza, for whose show in London they were a support band as well as a backing band.
Sadly they stopped their recording and touring activities in 1991; but some of the 'family' members are still involved in world music by producing CDs or running record companies. Lu Edmonds (aka Uncle Patrel) and Ben are in Billy Braggs' Blokes.
See also Ben Mandelson's interview in "Folk Roots" No. 26 (Aug., 1985) and 'World of Mustapha' in "Folk Roots" No. 77 (Nov., 1989).