We consider the viability problem for nonlinear evolutions inclusions of the form u′(t) ∈ Au(t) + F(u(t)), where A is an m-dissipative (possible nonlinear and multi-valued) operator acting in a Banach space X, K⊆X is a nonempty, locally closed set and $F:K{\user1{ \rightsquigarrow }}X$ is with nonempty, convex, closed and bounded values. We define the concept of A-quasi-tangent set to K at a given point ξ ∈ K and we prove a necessary condition for C 0-viability expressed in terms of this new tangency concept. We next show that, under various natural extra-assumptions, the necessary condition is also sufficient. We extend the results to the quasi-autonomous case, we deal with the existence of noncontinuable or even global C 0-solutions and, as applications, we deduce a comparison result and a sufficient condition for null controllability.