Semi-competing risks data include the time to a nonterminating event and the time to a terminating event, while competing risks data include the time to more than one terminating events. Our study is motivated from a prostate cancer study, which has one nonterminating event and two terminating events with both semi-competing risks and competing risks present. In this paper, we propose a new cure rate frailty model for this type of survival data. The proposed model is theoretically and computationally attractive. In addition, the proposed model can easily accommodate non-informative right-censoring times for the nonterminating and terminating events. Properties of the proposed model are examined in detail and an efficient Markov chain Monte Carlo sampling algorithm is alsodeveloped. The proposed methodology is further assessed using simulations as well as an analysis of real data from a prostate cancer study. This is a joint work with Mário de Castro, Yuanye Zhang, and Anthony V. D'Amico.