Tinariwen is unlike any musical group in the world, not just because of where they live (in a remote Malian town called Kidal), but because of their connection to armed rebellion, and because of their intense, guitar-driven songs. Almost unanimously, pop music critics in the West have labeled Tinariwen's output "desert blues," but that description doesn't convey the group's depth of sound, which produces twangy exaltations -- slow and fast - - that could just as well be compared to American rock 'n' roll or Arabic music.

"Our music shouldn't be called 'desert blues,' " says Abdallah Ag al- Housseini, a guitarist with Tinariwen, which is performing in Santa Cruz on Sunday and San Francisco on Tuesday as part of the group's first U.S. tour. "It's a term coined by Americans. Tamashek people used the term to be recognized in the West, but we want to be known as Tamashek people."

Tinariwen has played music for more than 20 years, but it's only been since 2001, when "The Radio Tisdas Sessions," its first international album, was released, that the group captured an audience far beyond its home in West Africa. Fifteen years ago, Tinariwen couldn't even think about performing (as it does now) in London and Paris. Then, its lead singer, Ibrahim Ag al-Habib, was in jail for his role in a rebellion of the Kel Tamashek people, who were fighting for more rights in Mali. In fact, al-Habib and others formed the group while they were in a squalor rebel camp in Libya, where they learned to shoot guns. Their music was protest music. Instead of real guitars, they played with makeshift instruments made from oil cans and other found objects. They based their songs completely on Kel Tamashek culture. Before Tinariwen's arrival, guitar music was virtually unknown among the Kel Tamashek. Tinariwen's name means "the deserts" in the Tamashek language.

"Our music doesn't come from Malian traditional music or from blues or from outside sources," says al-Housseini, speaking on the phone from France, where Tinariwen performed before embarking on its American tour. "The music basically came upon itself, because it was a way of reflecting the suffering and the pain of the Kel Tamashek people. In that sense, it does have a resemblance to blues, since blues came out of the suffering of the people. But in terms of musical influence, it is just what happened to us."

During the Kel Tamashek rebellion, which lasted on and off until the mid- 1990s, Tinariwen's music was banned in Mali. A peace accord in 1996 meant that members of Tinariwen and other Kel Tamashek people could try to integrate themselves into Malian society. Mali is one of the world's poorest countries, but it also has a rich musical culture that has produced some of world music's biggest names, including Ali Farka Toure, Oumou Sangare and Salif Keita. During the recording of the "The Radio Tisdas Sessions" in Kidal, the town's electricity only worked sporadically, forcing the album's producers to improvise the sessions. On Tinariwen's latest work, "Amassakoul" (which was released this month in the United States), the producers took no chances: They recorded most of the songs in Mali's capital, Bamako, then mixed them in a studio in France. The album has more noticeable influences from the West, as on the song "Arawan," which is a kind of rap song in Tamashek and French. The song still retains Tinariwen's trademark lyrics, which talk about the struggles of desert life.

"Nobody cares about the people of the desert who are suffering from thirst," goes the song, which features the type of ululations that Arab women do at weddings.

The voices of the men in Tinariwen are deep and almost haunting. It's another appealing aspect of the group's music. You can hear the years of experience in al-Habib's voice. It's a voice of wisdom and pain. He doesn't seem to be pretending when he says on the song "Ténéré Daféd Nikchan," "Tonight I sleep in the ruins. I follow the traces of my past. It sometimes befalls me to live like this."

Say al-Housseini, 36, speaking in words that are translated from French to English: "I remember the rebellious times. ... Our music still aims to address the issue of rebellion and what happened during the 1990s. Our mission is to let people know the message of the Tamashek people. We've been working for years to be able to go (outside of West Africa) to express the message of our people."