In a real separable Hilbert space, we consider nonautonomous
evolution equations including time-dependent subdifferentials and
their nonmonotone multivalued perturbations. In this paper, we
treat the multivalued dynamical systems associated with
time-dependent subdifferentials, in which the solution is not
unique for a given initial state. In particular, we discuss the
asymptotic behaviour of our multivalued semiflows from the
viewpoint of attractors. In fact, assuming that the
time-dependent subdifferential converges asymptotically to a
time-independent one (in a sense) as time goes to infinity, we
construct global attractors for nonautonomous multivalued
dynamical systems and its limiting autonomous multivalued
dynamical system. Moreover, we discuss the relationship between
them.