Didier Malherbe was born in Paris on January 22, 1943. He took up the saxophone at thirteen after hearing Charlie Parker's "Bloomdido," the title he would later carry as a stage name. After two years of formal lessons he was sitting in at Paris jazz clubs, playing with the bassist Alby Cullaz, the drummer Jacques Thollot and the organist Eddy Louiss. He came to find bebop puzzling for all its rules, and free jazz, which discarded them, did not hold him either: he decided to look elsewhere for his music.

In 1962, after hearing Ravi Shankar's first album, he travelled to India and learned the bansuri, the Indian bamboo flute. Back in Paris he studied ancient languages and classical flute at the Sorbonne. In 1964 and 1965 he lived in a community of musicians in Tangier, playing alongside the guitarist Davey Graham and picking up the basics of Arabic music. In 1966 he played saxophone with Les Rollsticks in Marc'O's musical comedy Les Idoles, which was filmed in 1968. In the summer of 1968 he moved to Majorca and lived on the property of the writer Robert Graves, where he spent time with Kevin Ayers and Daevid Allen.

He returned to Paris in 1969 and joined a raga-blues-folk trio called Morning Calm. That year he also played free jazz with the American pianist Burton Greene on an album for BYG, the label that issued Gong's first album, Magick Brother. Gong played its first concert at the Amougies festival in October 1969, and Allen gave Malherbe the stage name Bloomdido Bad de Grasse, a fusion of the Parker title and a joke on his surname. His saxophone and flute ran through the albums that made Gong's reputation: Camembert Electrique (1971), the soundtrack Continental Circus (1972) for Jérôme Laperrousaz's film, and the Radio Gnome Invisible trilogy on Virgin, Flying Teapot and Angel's Egg (both 1973) and You (1974).

When Allen and Steve Hillage left in 1975, Gong swung toward jazz-fusion, with Weather Report cited as an influence, and Malherbe stayed on and added world-music color, notably the piece "Bambooji" on Shamal (February 1976). On Gazeuse! (late 1976), the vibraphone-led jazz-fusion record made under Pierre Moerlen, he played tenor saxophone on two tracks and flute on one, alongside the guitarist Allan Holdsworth. He then formed Bloom, a band that fused jazz and rock and toured France, and released the album Bloom in 1979. In 1982 he teamed with Faton Cahen, a former pianist with Magma and Zao, in Faton Bloom, which made an album in 1986. He also worked with the singer Jacques Higelin on stage and on the album Aï (1985) and played on the debut by Equip'Out, the band of the former Gong drummer Pip Pyle.

His solo records of the 1990s moved steadily toward world music. Fetish (1990) used the Yamaha WX7 wind synthesizer. Zeff (Tangram, 1992) was built around the sound of a bent PVC pipe, the zeff, which also turned up in Vangelis's score for Ridley Scott's 1492: Conquest of Paradise, and was a critical and commercial success. Fluvius (1994) used a quartet with Loy Ehrlich, Henri Agnel and Shyamal Maitra. In 1996 he formed Hadouk with Ehrlich, the name joining the hajhouj, the Gnawa bass of Morocco that Ehrlich plays, and the duduk, the Armenian double-reed oboe that has been Malherbe's favorite instrument since 1995. Through those years he also toured with Classic Gong in Europe and the United States, left the band in 1999, and later returned as a guest on Zero to Infinity (2000) and 2032 (2009). He recorded with Brigitte Fontaine on Les Palaces and with the guitarist Pierre Bensusan on Live at the New Morning (1997).

In 1999 the American percussionist Steve Shehan joined the duo and the group became the Hadouk Trio. Its studio albums were Shamanimal (1999), Now (2002), Utopies (2006) and Air Hadouk (2010), and it also released the live records Live à FIP (2004) and Baldamore (2007), taken from two nights at Paris's Cabaret Sauvage in May of that year. The trio played jazz festivals including Nancy Jazz Pulsations and Jazz sous les Pommiers and, in 2007, won the Victoires du Jazz award for French instrumental artist or group of the year. In 2001 Djivan Gasparyan invited Malherbe to the international duduk festival in Armenia, and the same year he published L'Anche des Métamorphoses, a book of sonnets about reeds that became a solo show mixing poetry and music.

A duo with the guitarist Éric Löhrer produced Nuit d'Ombrelle (2011), a double album that sets jazz standards played on duduk beside improvisations in one continuous suite. From 2012 he played with the classical pianist Jean-François Zygel on Zygel's France 2 program La Boîte à Musique and performed in a trio with the percussionist Joël Grare under the title A World Tour in 80 Minutes. The Hadouk Quartet, with Löhrer and the percussionist Jean-Luc Di Fraya, formed in 2013 and released Hadoukly Yours on November 4 of that year and Le Cinquième Fruit in 2017. Le Concile des Oiseaux (2024), a duo record with Ehrlich, closed the cycle the two began in the 1990s. On September 15, 2026 he released Cheerful Pendulum on Tribal Zik Records, an album with the multi-instrumentalist Raphaël Didjaman on which he plays duduk and bawu.

Malherbe's fame rests on Gong, and the honest label for his career is jazz-rooted rather than simply jazz: he learned the saxophone from Charlie Parker records and Paris jam sessions, built his reputation in psychedelic and progressive rock, and since the mid-1990s has worked in a world-music setting that French sources file as ethno-jazz or world jazz. AllMusic lists his genres as both Pop/Rock and Jazz and tags his styles as Canterbury Scene, Fusion, Global Jazz and Post-Bop, which matches the split. His music is built from reeds and breath rather than from bebop vocabulary: soprano saxophone, flutes and the bansuri from his Indian studies, and since the 1990s the duduk, alongside the Chinese bawu and hulusi, ocarina and the Laotian khene. The influences are travel and collaboration as much as records: Parker first, then Ravi Shankar, the Moroccan music he heard in Tangier, Daevid Allen's circle in Majorca, and the Armenian duduk tradition of Gasparyan. He is also a published poet, with two books of sonnets, and has built shows around spoken verse and music.