Abstract.Most of the existing work in non‐linear time series analysis has concentrated on generating flexible functional models by specifying non‐linear specifications for the mean of a particular process, without much, if any, attention given to the distributional properties of the model. However, as Martin (J. Time Ser. Anal.13 (1992), 79–94) has shown, greater flexibility in perhaps a more natural way can be achieved by consideration of distributions from the generalized exponential class. This paper represents an extension of the earlier work of Martin by introducing a flexible class of non‐linear time series models which can capture a wide range of empirical behaviour such as skewed, fat‐tailed and even multimodal distributions. This class of models is referred to as generalized exponential non‐linear time series. A maximum likelihood algorithm is given for estimating the parameters of the model and the framework is applied to estimating the distribution of the movements of the ex