This article presents a method for analyzing repeated measures with categorical responses based on maximizing a conditional likelihood. Many existing methods for analyzing repeated categorical responses, such as those proposed by Duncan (1980, 1985), Bishop, Fienberg, and Holland (1975), and Cochran (1950) are special cases of the method based on the conditional likelihood approach. This article explores the relationships among the various methods and extends several of the existing methods. The conditional likelihood approach is used to analyze data from a four-wave panel study with trichotomous responses. The data, taken from Fienberg, Bromet, Follmann, Lambert, and May (1985), are from an investigation of the psychological effects of the accident at the Three Mile Island nuclear power plant in the spring of 1979. In this example, methods are presented for checking the assumption of local independence in the model used for the conditional likelihood analysis. With an extension of the results of Tjur (1982), it is demonstrated that the conditional estimates can be obtained with standard statistical software.