A suboptimal dual adaptive system is developed for control of stochastic, nonlinear, discrete time plants that are affine in the control input. The nonlinear functions are assumed to be unknown and neural networks are used to approximate them. Both Gaussian radial basis function and sigmoidal multilayer perceptron neural networks are considered and parameter adjustment is based on Kalman filtering. The result is a control law that rakes into consideration the uncertainty of the parameter estimates, thereby eliminating the need to perform prior open-loop plant identification. The performance of the system is analyzed by simulation and Monte Carlo analysis.