The variational convergence of sequences of optimal control problems
with state constraints (namely inclusions or equations) with weakly converging input
multi-valued operators is studied in a nonre\ub0exive abstract framework, using \ua1-conver-
gence techniques. This allows to treat a lot of situations where a lack of coercivity forces
to enlarge the space of states where the limit problem has to be imbedded. Some concrete
applications to optimal control problems with measures as controls are given either in a
nonlinear multi-valued or nonlocal but single-valued framework
