The general \(N\)-stage nonlinear stochastic optimal control problem is treated in an approximate way using multilayer feedforward neural networks. After presentation of the problem statement and the basic assumptions, it is shown that an approximative solution may be reached by prescribing a limited-memory control law with a number of free parameters which transforms the originally stochastic optimal control problem into a stochastic nonlinear programming problem. Next, a limited-memory multilayer neural function is employed as a fixed-structure control law with the neural weights being the free control parameters. Some properties of neural function control law approximators are established that motivate this choice against other functional approximators. A stochastic gradient-type technique (back propagation), based on the computation of stochastic variable realizations, is employed to solve the nonlinear programming problem which leads to an approximate specification of the neural weights. The overall technique is applied, for demonstration purposes, to two example problems, namely an LQG-problem with known optimal control law and a freeway traffic optimal control problem.