For some diseases there is evidence that infected individuals reach different levels of infectiousness and remain infectious for different periods of time. When the underlying reasons for such heterogeneity are not well understood it becomes difficult to implement the classification of infectives necessary for the use of the multi-parameter chain binomial model. It is then necessary to introduce random variables to explain the heterogeneity. In this chapter we discuss epidemic chain models which result when either heterogeneity between individuals or heterogeneity between households is explained by taking the parameters of certain chain binomial models as random variables. It should become apparent that the models of Chapter 2 are essentially fixed effects models while the models of this chapter are random effects models. Here we use the terms ‘fixed effects’ and ‘random effects’ in the same sense as they are used in the standard analysis of variance.