The paper describes and evaluates three methods of modelling earthquake accelerograms using artificial neural networks and linear predictors. These are a radial-Gaussian neural networking system, a linear predictor, and a hybrid of these two. Two methods of using these models to predict ground acceleration are adopted. The first is based on a direct prediction of ground acceleration at some point in time in the future from a series of ground accelerations that occurred earlier in the earthquake event. The second is a recursive approach whereby a model predicts a sequence of future ground accelerations by feeding back its predictions to its inputs. The performances of the models are tested using the 1985 Mexico earthquake and aftershock. The linear predictor and hybrid models perform best at direct prediction while none of the models perform particularly well at recursive prediction. The paper concludes with an outline of some areas for future work.