Adaptive neural predictive control strategies for general nonlinear systems are proposed. The network weight update rule with discrete-time learning procedures which executes the minimal error between the feedforward neural network (FNN) model output and plant output is obtained. The one-step-ahead neural predictive control combined with the 'dual' optimization algorithm serves as a rapid, reliable adaptation mechanism and guarantees the stable output regulation of a class of uncertain nonlinear systems. In principle, the off-line training algorithm on neural networks is reduced, and the state/parameter estimation design is obviated. Through closed-loop simulation demonstrations, the proposed control schemes have been successfully applied to two reactor system examples.