Marmosets are emerging rapidly as experimental models for studying the neural bases of cognition and, importantly, for modeling disorders of human cognition, but many aspects of their mental attributes remain to be characterized. When judging elapsed time, humans implicitly use prior information to predict upcoming events and reduce perceptual and decision-making uncertainty. An influential model of temporal expectation is the hazard rate model, which posits the likelihood of an event occurring in the future, provided it has not occurred already. Here, we report that marmosets trained on a reaction time task acquire the hazard rate model of expectation, consistent with the global task structure. The model emerges progressively with learning but unexpectedly continues to be modified by local contingencies, as demonstrated by a serial effect of trial duration on responses. The combined effects of global and local task structure are well described by a multiple regression model and computationally by Bayesian updating of the hazard function. Parallel experiments in human subjects similarly demonstrate global followed by local influences on reaction times and temporal expectation. Thus, in both marmosets and humans, task history and local structure continuously update task-specific responses, surprisingly at the expense of optimal responses after the competent acquisition of an internal model.