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The irreversible illness-death model describes the pathway from an initial state to an absorbing state either directly or through an intermediate state. This model is frequently used in medical applications where the intermediate state represents illness and the absorbing state represents death. In many studies, disease onset times are not known exactly. This happens for example if the disease status of a patient can only be assessed at follow-up visits. In this situation the disease onset times are interval-censored. This article presents the SmoothHazard package for R. It implements algorithms for simultaneously fitting regression models to the three transition intensities of an illness-death model where the transition times to the intermediate state may be interval-censored and all the event times can be right-censored. The package parses the individual data structure of the subjects in a data set to find the individual contributions to the likelihood. The three baseline transition intensity functions are modelled by Weibull distributions or alternatively by M -splines in a semi-parametric approach. For a given set of covariates, the estimated transition intensities can be combined into predictions of cumulative event probabilities and life expectancies.