A neural network scheme for modelling unknown nonlinear systems subject to immeasurable disturbances that satisfy stable, finite-order, recurrence relationships whose parameters are known is presented. The systems considered can be expressed as nonlinear ARMAX models and the disturbance is nonstochastic. Similar to robust servomechanism design, the nonlinear modes of the disturbances are assumed to be known and based on the knowledge of these modes; a new performance function for modelling the unknown nonlinear function is selected and a gradient descent algorithm which adjusts the weights in the neural network is derived. Convergence of this learning algorithm is proved when the disturbance satisfies a linear recurrence relationship, and the proposed approach is used to model nonlinear time series data which has been corrupted by immeasurable additive sinusoidal noise.