  The celebrated Kadison--Sakai theorem states that every derivation on a von
Neumann algebra is inner. In this paper, we prove this theorem for ultraweakly
continuous *-\sigma-derivations, where \sigma is an ultraweakly continuous
surjective *-linear mapping. We decompose a $\sigma$-derivation into a sum of
an inner \sigma-derivation and a multiple of a homomorphism. The so-called
*-(\sigma,\tau)-derivations are also discussed.
