The problem of estimating a smooth distribution function F at a point γ 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(γ). It is shown that the relative deficiency of the Kaplan-Meier estimator of F(γ) with respect to the appropriately chosen kernel type estimator 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.