In this paper, stochastic processes developed by Aalen [1] [2] are adapted to the Nelson-Aalen and Kaplan-Meier [3] estimators in a context of competing risks. We focus only on the probability distributions of complete downtime individuals whose causes are known and which bring us to consider a partition of individuals into sub-groups for each cause. We then study the asymptotic properties of nonparametric estimators obtained.