Aperiodic automorphisms of nuclear purely infinite simple C*-algebras

We show that if two aperiodic automorphisms of a separable nuclear unital p urely infinite simple C*-algebra are asymptotically unitarily equivalent, t hen they are outer conjugate with respect to an automorphism which is isoto pic to the identity automorphism. Thus, by Kirchberg and Phillips, they hav e the same KK-class if and only if they are outer conjugate with respect to an automorphism which is in the KK-class of the identity automorphism.