: A survey is given of recently developed models for continuous variate non–Gaussian time series. The emphasis is on marginally specific models with given correlation structure. Exponential, Gamma, Weibull, Laplace, Beta and Mixed Exponential models are considered for the marginal distributions of the stationary time series. Most of the models are random coefficient, additive linear models. Some discussion of the meaning of autoregression and linearity is given, as well as suggestions for higher–order linear residual analysis for non–Gaussian models.