The class of autoregressive conditional duration (ACD) models plays an important role in modelling the duration data in economics and finance. This paper presents a non-linear model to allow the first four moments of the duration to depend nonlinearly on past information variables. Theoretically the model is more general than the linear ACD model. The proposed model is fitted to the data given by the 3534 transaction durations of IBM stock on five consecutive trading days. The fitted model is found to be comparable to the Weibull ACD model in terms of the in-sample and out-of-sample mean squared prediction errors and mean absolute forecast deviations. In addition, the Diebold-Mariano test shows that there are no significant differences in forecast ability for all models
