(eng): We consider parameter-dependent mathematical programs with constraints governed by the generalized non-linear complementarity problem and with additional non-equilibrial constraints. We study a local behaviour of stationarity maps that assign the respective C- or M-stationarity points of the problem to the parameter. Using generalized differential calculus rules, we provide criteria for the isolated calmness and the Aubin properties of stationarity maps considered. To this end, we derive and apply formulas of some particular objects of the third- order variational analysis.