Adapting certain methods of Voiculescu we show that the quasidiagonali
ty of C-algebras is invariant under completely positive deformations
coming From asymptotic morphisms. We define a notion of quasidiagonal
morphism. The quasidiagonality of morphisms from exact separable C-al
gebras is shown to be invariant under completely positive deformations
. (C) 1997 Academic Press.