Summary. A method of constructing trees for correlated failure times is put forward. It adopts the backfitting idea of classification and regression trees (CART) (Breiman et al., 1984, in Classification and Regression Trees). The tree method is developed based on the maximized likelihoods associated with the gamma frailty model and standard likelihood-related techniques are incorporated. The proposed method is assessed through simulations conducted under a variety of model configurations and illustrated using the chronic granulomatous disease (CGD) study data.