  This paper studies stability aspects of solutions of parametric mathematical
programs and generalized equations, respectively, with disjunctive constraints.
We present sufficient conditions that, under some constraint qualifications
ensuring metric subregularity of the constraint mapping, continuity results of
upper Lipschitz and upper H\"older type, respectively, hold. Furthermore, we
apply the above results to parametric mathematical programs with equilibrium
constraints and demonstrate, how some classical results for the nonlinear
programming problem can be recovered and even improved by our theory.
