Dynamic Bayesian models are developed for application in nonlinear, non-normal time series and regression problems, providing dynamic extensions of standard generalized linear models. A key feature of the analysis is the use of conjugate prior and posterior distributions for the exponential family parameters. This leads to the calculation of closed, standard-form predictive distributions for forecasting and model criticism. The structure of the models depends on the time evolution of underlying state variables, and the feedback of observational information to these variables is achieved using linear Bayesian prediction methods. Data analytic aspects of the models concerning scale parameters and outliers are discussed, and some applications are provided. Dynamic Bayesian models are developed for application in nonlinear, non-normal time series and regression problems, providing dynamic extensions of standard generalized linear models. A key feature of the analysis is the use of conjugate prior and posterior distributions for the exponential family parameters. This leads to the calculation of closed, standard-form predictive distributions for forecasting and model criticism. The structure of the models depends on the time evolution of underlying state variables, and the feedback of observational information to these variables is achieved using linear Bayesian prediction methods. Data analytic aspects of the models concerning scale parameters and outliers are discussed, and some applications are provided. © 1985 Taylor & Francis Group, LLC.