Stochastic programs form a class of optimization problems that have seen much attention in the last decade. As has the class of equilibrium problems which have resulted largely from the analytic treatment of Nash games. This thesis delves into some challenging areas of stochastic optimization and stochastic equilibrium programming. Our interest is in understanding properties of these problems and in developing algorithms for solving such problems. We first consider a two-period stochastic nonlinear program. In this context, we obtain new insights into the notions of feasibility and recourse...