In medical research, investigators often wish to characterize the distributions of remaining lifetimes. While nonparametric analyses of residual life distributions have been widely studied with independently right-censored data, residual life analysis has not been examined in the competing risks setting, with multiple, potentially dependent, failure types. We define the cause-specific residual life distribution as the residual cumulative incidence function conditionally on survival to a given time. Because of the improper form of the cause-specific distribution, the mean cause-specific residual lifetime does not exist, theoretically. We develop nonparametric inferences for the cause-specific residual life function and its corresponding quantiles, which may exist. Theoretical justification, including uniform consistency and weak convergence, is established. Simulation studies and a breast cancer data analysis demonstrate the practical utility of the methods.