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This paper introduces a novel adaptive neural network compensator for feedforward compensation of external disturbances affecting a closed loop system. The neural network scheme is posed so that the nonlinear disturbance model for a measurable disturbance can be adapted for rejection of the disturbance affecting a closed loop system. The non-linear neural network approach has been particularly developed for 'mobile' applications where the adaptation algorithm has to remain simple. For that reason, the theoretical framework justifies a very simple least-mean-square approach suggested in a mobile hard disk drive context. This approach is generalized to a non-linear adaptive neural network compensation scheme. In addition, usual assumptions are relaxed, so that it is sufficient to model the nonlinear disturbance model as a stable system avoiding strictly positive real assumptions. The output of the estimated disturbance model is assumed to be matched to the compensation signal for effectiveness, although for stability this is not necessary. Simulation examples show different features of the adaptation algorithm also considering a realistic hard disk drive simulation.