In this paper and its companion, the identification of mathematical models describing the behaviour of wave energy devices (WECs) in the ocean is investigated through the use of numerical wave tank experiments. When the wave amplitude and the WEC displacement are not negligible with respect to the WEC dimensions, nonlinear hydrodynamic effects may appear, and the accuracy of linear hydrodynamic models is reduced, leading to the necessity of introducing some nonlinearities in the model structure. This paper proposes, for WEC modelling, the use of discrete-time nonlinear autoregressive with exogenous input (NARX) models, as an alternative to continuous-time models. Techniques of model identification are also explained and applied to a case study.