I originally intended to get this post up before the Insubordination post. Here is the background and context of the dispute between ISI and the Al Nusra Front.
On June 9th, Al Jazeera published a letter, purportedly from Ayman al Zawahiri, addressed to the Abu Bakr al Baghdadi, the emir of the Islamic State of Iraq, and Abou Muhammad al Julani, the emir of Jabhaat al Nusra. According to the Long War Journal, US intelligence considers the letter to be genuine.
On April 8th, al Baghdadi (also known as Abu Dua) announced the formation of the Islamic State in Iraq and the Levant by audio message, claiming that ISI and al Nusra were now under his one, over-arching organization. He claimed that al Julani had been trained and deputized by the Islamic State of Iraq (the new brand name for al-Qaeda in Iraq) and that therefore it was appropriate that the connection between the groups be acknowledged, and they both fall under the same command.
Only a few days later, al Julani issued his own message, rejecting the new name. He swore allegiance directly to Ayman al Zawahiri, effectively establishing that he holds an independent command, and does not answer to al Baghdadi. According to Al Jazeera, the dispute has led to defections and a breakdown in operational capability as infighting started between the two branches.