Deterministic learning theory was presented and investigated recently. Due to the existence of time varying disturbances, learning capability may be influenced. In this paper, deterministic learning theory will be analyzed in environments with disturbances. With appropriately designed adaptive neural controller, the disturbances are attenuated and partial persistent excitation (PE) for radial basis function neural network (RBF NN) is satisfied. By utilizing partial PE condition and uniform complete observability (UCO) technique, the nominal part of the error subsystem is exponentially stable. Furthermore, all signals of the error subsystem converge to a neighborhood of zero exponentially and the size of the neighborhood relies not only on the amplitude of disturbances but also on the control gains. After the learning process, the estimated neural weights are stored in RBF NN and a constant neural controller can be implemented. The simulation shows the effectiveness of this scheme.