Successful identification procedures are undoubtedly important for accurate model description and the consequent implementation of control strategies. Linear Parameter Varying (LPV) models are nowadays standard for control design purposes and powerful identification techniques accordingly available. Anyhow, recent advances have brought to focus the class of Nonlinear Parameter Varying (NLPV) models, which keep some nonlinearities embedded to the formulation. Identification tools for this latter class are still not available. Therefore, this paper proposes a novel method for the robust identification of stochastic NLPV systems, considering that the nonlinear parameter part is a priori known and obeys a Lipschitz condition. The method is based on a modified extended Masreliez-Martin filter and yields the joint estimation of both NLPV systems states and model parameters. The method manages the stochasticity of the system by considering the presence of measurement outliers with non-Gaussian distributions. Results considering real data from a vehicle suspension system are presented in order to demonstrate the consistency of the proposed method.