The document, part of a series of chapters described in SO 011 759, examines sociological research methods for the study of change. The advantages and procedures for dynamic analysis of event-history data (data giving the number, timing, and sequence of changes in a categorical dependent variable) are considered. The authors argue for grounding this analysis in a continuous-time stochastic model. This approach permits the data to be fully utilized and allows a unified treatment of the many approaches that use only part of the information of this data. The report focuses on the familiar continuous-time Markov model, summarizes its properties, reports its implications for various outcomes, describes extensions to deal with population heterogeneity and time-dependence, and outlines a maximum likelihood procedure for estimating the extended model from event-history data. The discussion is illustrated with an empirical analysis of the effects of an income maintenance experiment on change in marital status. Event-history analysis is contrasted with cross-sectional, event-count, and panel analyses. The conclusion is that event-history analysis has substantial advantages over these other approaches. (Author/KC)