AbstractA class of doubly stochastic Poisson processes, which is termed a Markov‐modulated Poisson process, is studied. The maximum likelihood method is used to make inferences about the Markov‐modulated Poisson process. Expressions are derived for the likelihood function and for second‐order properties of both counts and intervals. A simple two‐state model is applied to a set of exposure data and to simulated data. Bivariate generalization of this process is also studied.