Mixture cure models can be used to analyze time-to-event data when there is a non-susceptible group of patients who are not at risk for the event. The model is particularly applicable for cancers where it is believed that some patients can be cured and will not experience a recurrence of the cancer. Competing risks, such as death from other causes, are common and may prevent observation of the recurrence. The multistate cure model, which allows for competing risks, is a natural extension of the cure model. The multistate cure model specifies a model for the probability of cure and three intensity processes for the transitions from initial state to recurrence, from initial state to death, and from recurrence to death. The model can include baseline covariates that can affect the probability of cure and the intensity processes in different ways, which can enhance interpretation. Monte Carlo EM and Bayesian methods can be used for estimation. A common occurrence is unequal censoring times for recurrence and death. For this, we propose to impute recurrence events for those who are censored for recurrence before death. The methods will be applied to head and neck cancer data.