A new and more general asymptotic condition for scattering systems is formulated. It is based on a physically motivated topology in the set of all states. This topology turns out to be the same as that induced by the trace norm. The existence of wave operators is demonstrated in this more general setting and the relation of these generalized wave operators to the conventional ones is clarified. A simple example is mentioned of a system which satisfies the new but not the old asymptotic condition.