The problem of estimating a smooth distribution function F at a point $ au$ based on randomly right censored data is treated under certain smoothness conditions on F . The asymptotic performance of a certain class of kernel estimators is compared to that of the Kap lan-Meier estimator of F($ au$). It is shown that the .elative deficiency of the Kaplan-Meier estimate. of F($ au$) with respect to the appropriately chosen kernel type estimate. tends to infinity as the sample size n increases to infinity. Strong uniform consistency and the weak convergence of the normalized process are also proved.