The Cox proportional hazard model is the most widely used model in activity episode duration analysis. A potentially limiting underlying assumption of this model class is that the explanatory variables have a proportional effect on the hazard function. There is no direct relationship between the covariates and time itself. An alternative model class, not characterized by this assumption, is the accelerated hazard (AH) model. The coefficients in this model class reflect variations of hazard rates over time, which are accelerated or decelerated. Another issue is the problem of heterogeneity. Cox proportional hazard models that include heterogeneity are now well known. Including heterogeneity in the AH model is more complicated and under-explored, but potentially more rewarding. The paper uses a latent class specification for the AH model to capture heterogeneity and propensity to accelerate (or decelerate) activity durations. The use of a latent class specification is beneficial for representing individual/household response differences (accelerate/decelerate their current activity durations) to transportation policy. Such information may be useful to transportation engineers or planners when targeting their policies. To contribute to this research frontier, the present paper reports their results of the development of the first latent class accelerated hazard (LCAH) model in transportation which is applied to activity diary data on three out-of-home activities (daily shopping, non-daily shopping and out-of-home leisure) and two in-home activities (in-home task and in-home leisure), collected in Eindhoven, The Netherlands. The results of the LCAH model suggest that heterogeneity is strongly related to sociodemographic variables. The presence of children and the employment status of the female spouse are the most important factors explaining heterogeneity among the derived latent classes.