Parametric nonlinear evolution inclusions driven by time-dependent subdifferentials are considered. First some continuous dependence results are proved for the solution set (of both the convex and non-convex problems) and for the set of solution-selector pairs (of the convex problem). Then a continuous version is derived of the Filippov-Gronwall inequality, using which the parametric relaxation theorem is proved. An example of a parabolic distributed parameter system is also worked out in detail