"Kull tore the veil away with one motion and recoiled with a gasp. (...) The face of the man was a bare white skull , in whose eye sockets flamed livid fire!" -- Robert E. Howard: "Delcardes' Cat"
In Kull's time, 8,000 years before the time of Conan, Thulsa Doom was already an undead sorcerer. The flesh of the skull-faced wizard was that of a man long dead, and normal weapons could not harm him.
In that time, his were the gifts of illusion, planar travel, and of invisibility, which only he possessed.
Thulsa Doom serves the Great Serpent and is the master of the serpent people. In the time of Valusia, his sworn enemy was King Kull, who broke the power of the serpent-men.
The undead sorcerer returned in Conan's time, when the barbarian unwittingly rescued him from the pits of Arallu. Later, Conan separated Thulsa's physical body from his skull.
Now, Thulsa's form is that of a grinning skull with the powers of telepathy, levitation and summoning of demonic servants. Until his body is restored, Thulsa is somewhat limited to defensive sorcery. His current enemy is Thoth-Amon, with whom he contends for control over the serpent-men.