Led Zeppelin luminary Robert Plant says that listening to their music is like dropping a bucket into a deep well. And bluesman Taj Mahal, when he first heard them, said he felt like he'd come home.

Tinariwen are getting used to such tributes. Appreciation for their brand of blues from the southern Sahara has been picking up over the past five years. Billy Kelly, the promoter behind Glasgow's Big Big World festival and one of the band's early champions, said they communicated something; what it was he couldn't quite put his finger on, but it was there all right.

Tinariwen's spokesman, Abdallah Ag Alhousseyni, empathises with Kelly. Back in the late 1970s and early 1980s, they used to listen to bootleg cassettes of American music which had little or no information on the cover. None of the band spoke English, so they'd hear this music and love it without understanding it all. "Which is probably how a lot of people outside the desert are hearing Tinariwen now," he laughs.

Sadly, Billy Kelly died suddenly at the beginning of February - but the Scottish Arts Council Tune-Up tour that he instigated and organised is going ahead next week in his honour, with Tinariwen as special guests. The Scottish concerts form part of a European trek of more than 50 dates - but the band have grown used to international touring over the past five years, and make the most of it. "When we were younger and living in the desert, we often dreamed of travelling all over the world," says Abdallah. "But those were the kind of dreams that you never really imagine might come true. When the group started, we were concentrating on raising awareness among the desert people. Now we're doing the same throughout the world."

Tinariwen got together in 1979 in Tamanrasset, Algeria, when guitarist Ibrahim Ag Alhabib, forced into exile by the Malian government's expulsion of his people, the Touareg, got together with two friends from the same part of the desert in north-eastern Mali. As a youngster, Alhabib had begun playing music on home-made guitars, plucking out traditional Touareg melodies and north-Malian blues.

"There was nothing really organised; it was just a group of friends passing the time or playing at weddings and round campfires out in the bush," says Abdallah of the original trio. "But the important thing is that they also started to write songs, which were very much about the current realities of their situation. This was a big change."

In the 1980s and into the early 1990s, Tinariwen, by now a large group of friends with various roles, musical and non-musical, became embroiled in rebellion in Algeria. Some of them joined the Libyan army; installed in barracks near Tripoli, they would play for their fellow troops. A collection was organised by the officer in charge and equipment bought. So, in a special room in the barracks, the band, now joined by Abdallah and poet and lyricist Japonais, began recording their songs on cassettes for anyone who wanted to listen.

"These cassettes would then be taken back to the villages and nomad camps out in the deep desert, and that's how the word spread," says Abdallah. "Many people heard Tinariwen without having the slightest idea who they were, where they came from, what they looked like or anything like that. It was a very clandestine grapevine. And then after the Tamanrasset Accords a peace effort in Mali in 1991, the band came out into the open. It was a big surprise for people!"

Now able to turn their attention to music full-time, Tinariwen began to play in all sorts of situations and for different audiences. They played at official events in the Malian capital, Bamako, and in Tripoli. Other gatherings, deep in the desert, were more informal and called for mobile electricity generators or amps that could run off car batteries. When motor transport wasn't available - the camel is still the main means of transport for the nomadic community - they had to play their gigs through battery-powered practice amps.

The group's big break came with the inaugural Festival in the Desert, which took place in the Sahara in 2001. After that, word began to spread internationally. Robert Plant, who also appeared at the festival, was particularly enthusiastic, and soon Tinariwen were touring and sharing festival stages with Plant, Taj Mahal and Carlos Santana, another high- profile fan.

Their modus operandi remains the same as before. Band members write independently and bring their songs to the group. After that they simply play them until they feel they're ready to be performed in public. The opening up of an international market for their songs hasn't altered their subject matter: Tinariwen's lyrics still reflect the Touareg people's lives, be they about love, loss, nostalgia, courage, identity, unity, peace, development or - a recurring theme - exile and the emotional pain it creates.

"We call that pain assouf'," says Abdallah. "It means nostalgia, longing, loneliness or separation. And it also means everything that is beyond the campfire, out there in the darkness of the empty desert.We believe very much in the spirit world, and the spirits who inhabit the desert are often known collectively as the Kef Assouf, the people of the darkness. There's a song on the new album called Assouf and it expresses the feeling very well. In fact, assouf is close to the word blues'. It means almost the same thing."

Singing the blues doesn't preclude their audience having a good time, though. "Oh no, if people just want to listen and dance, that's fine with us," says Abdallah. "Essentially what we want to put across is a feeling of joy, of happiness and of curiosity about the desert, about the Touareg and the problems of the Sahara. If that curiosity then turns into a will to find out more, or even to travel to the desert and make contact, I think we have done our job."