In this talk, we consider a competing risks model including covariates in which the observations are subject to random right censoring. Without any assumption of independence of the competing risks, and based on a nonparametric kernel-type estimator of the incident regression function an estimator of the conditional regression function is proposed. We show that at a given covariate value and under suitable conditions the nonparametric estimator of the regression function is asymptotically normal. A simulation study is provided showing that our estimators have good behavior for moderate sample sizes.