We study mixed hitting‐time models that specify durations as the first time a Lévy process—a continuous‐time process with stationary and independent increments—crosses a heterogeneous threshold. Such models are of substantial interest because they can be deduced from optimal‐stopping models with heterogeneous agents that do not naturally produce a mixed proportional hazards structure. We show how strategies for analyzing the identifiability of the mixed proportional hazards model can be adapted to prove identifiability of a hitting‐time model with observed covariates and unobserved heterogeneity. We discuss inference from censored data and give examples of structural applications. We conclude by discussing the relative merits of both models as complementary frameworks for econometric duration analysis.