This paper is a continuation and development of work on a group of latent structure models proposed by Lazarsfeld and Henry (1968) and Wiggins (1973) for analyzing processes of change over time. There have been problems associated with these models, see, e.g., Duncan (1975). In this paper a general framework for presenting such models is introduced. A latent class Morkov chain model is presented and its identification is discussed. Two Expectation-Maximization algorithms, corresponding to types of data (T-dimensional frequency tables and (T-1) frequency matrices associated with T points in time), are developed for estimation A model of independent latent random processes is presented as a special case. Two examples from sociometric study and voting intentions are re-analyzed for illustration. Models and methods developed have the following advantages. They are applicable to polytomous as well as dichotomous variables, for any number of time points. Procedures are provided for testing model goodness of fit, model selection and prediction. Estimates are maximum likelihood estimates and always lie between zero and one.