Although the Tuareg and Islamic militants have jointly driven out the Malian military from the northern area they are unable to agree on the nature of the newly declared independent Azawad.
The largest group is the Tuareg led National Movement for the Liberation of Azawad (NMLA). This group fought most of the major battles against the Malian military. However, as they advanced the Islamic militant group Ansar Dine joined in the fray. This group wants Azawad to be a Taliban style state under Sharia law.
On the other hand the Tuareg some of whom fought for Gadaffi want a secular state. Gadaffi of course persecuted radical Islmanists. Some claim that Ansar Dine has ties to Al Qaeda. I always take such claims with a grain of salt. Often this is used as a justification for U.S. aid or even involvment. There are already U.S. specail forces in Mali and the Malian military have been trained and provided aid by the U.S. One can expect a military move to oust the rebels after the political situation is sorted out down south.
A couple of months ago a U.S trained Capt. Sanogo led a successful military coup against the elected president. While he handed over power to a transitional civilian government he is still influential and of course was not punished for his actions.
The Tuareg want Azawad to ratify UN conventions on human rights and be a secular state. Both the Tuareg and Islamists have forces in major cities. So far they have avoided outright conflict. The groups no doubt realize they need unity to confront attempts by the Malian military to retake the territory. For more see this article.