Summary: Kojima's strong stability of stationary solutions can be characterized by means of first and second order terms. We treat the problem whether there is a characterization of the stability concept allowing perturbations of the objective function only, keeping the feasible set unchanged. If the feasible set is a convex polyhedron, then there exists a characterization which is in fact weaker than that one of strong stability. However, in general it appears that data of first and second order do not characterize that kind of stability. As an interpretation we have that the strong stability is the only concept of stability which both admits a characterization and works for large problem classes.