The National Crime Survey produces ongoing national data on crime victimization, based on a stratified multistage cluster sampling plan that uses a rotating panel of household locations. In March 1981, the Bureau of Justice Statistics, which sponsors the survey, issued a report on the prevalence of crime, in which the key quantity estimated is the percentage of households touched by crime in a given year. This paper describes some stochastic longitudinal models for victimization that can be used to produce such an annual prevalence rate, and it is shown how the reported prevalence measure relates to those derived from this study. The study develops several 'naive' stochastic longitudinal models in which missing data are assumed to be missing at random. The models are considered 'naive' because each is based on a large number of inappropriate but simplifying assumptions, and because they reflect little of the structure described in longitudinal analyses by Reiss (1980) and Fienberg (1980a, 1980b). Moreover, the models are fitted only to data on housing units or location and not to longitudinal files on persons in the household, and victimizations are treated in aggregate form. The intent in presenting such models and results from their preliminary application is to establish a starting point for future modeling that will use more appropriate and substantively interesting assumptions. The appendix describes the Bureau of Justice Statistics estimators. Tabular data and 16 references are provided.