The residual life has been used as a natural concept to describe time-to-event distributions for centuries. Popular summary measures to characterize a probability distribution of the residual lifetimes are the mean or quantile residual life function. However, the quantile function is preferred to summarize a residual life distribution, especially, under competing risks because the mean function does not exist theoretically in that case. A simple example of a competing risks analysis would be to infer the proportion of breast cancer related-deaths in the presence of non-breast cancer-related deaths due to heart failures, say. In this talk, we define the cause-specific residual cumulative incidence function and propose a test statistic to compare the quantile residual lifetimes between two groups. The proposed method is illustrated with a breast cancer dataset from a phase III clinical trial.