A class of recurrent events data, such as the incidence of hypoglycemia in a clinical trial of Type II diabetes treatments, can be modeled by renewal process of gap times. A feature often seen in such data is the alternating pattern of frequent and infrequent events within subject, and notable heterogeneity between subjects. Previous methodologies often fail to consider both sources of variability. We propose a new latent class gap time model that the frequent and infrequent events are modeled by two latent classes of correlated gap time distributions, and the switching between latent classes within subject are dictated by the probability of event recurrence after the previous one. It provides an alternative framework of analyzing complicated recurrent event data, which in the hypoglycemia example enables us to differentiate two diabetes treatments in latent patterns of recurrent events.