Recurrent alternating event data arise from studies in which subjects experience two different types of events alternately, for example, recurrent hospitalization of patients with a chronic disease. There has been few literature addressing this type of data. This research proposes a parametric approach by specifying the transition intensities of alternating events. Maximum likelihood estimators will be developed and its performance for practical sample sizes will be investigated. The research provides a departure point and benchmark for semiparametric and nonparametric approaches.