In this paper we consider a generalization of Kojima’s strong stability in nonlinear programs to variational inequalities constrained by a system of equations and inequalities. Roughly speaking, strong stability refers to the local existence and uniqueness of a solution cf a system under small perturbations. The purpose of the paper is to establish a new and complete characterization for strongly stable generalized Karush-Kuhn-Tucker points and to give a complete characterization for strongly stable stationary solutions under the Mangasarian-Fromovitz constraint qualification.