He is believed to have assumed many of the late Mohammed Atef's duties in al-Qaeda.
He was a colonel in the Egyptian army but joined the mujahideen fighting to expel the Soviets from Afghanistan.
He is also suspected of teaching militants to use explosives and training some of the 11 September hijackers.
He has been linked to the bombings of US embassies in Kenya and Tanzania in 1998. The US further accuses him of training the Somali fighters who killed 18 US servicemen in Mogadishu in 1993.
In 1987, Egypt accused Adel - whose real name is Muhammad Ibrahim Makkawi - of trying to establish a military wing of the militant Islamic group al-Jihad, and of trying to overthrow the government.