Abstract: In this paper, we use the so called counting process, developed by Aalen 1, to study the asymptotic normality of kernel estimates for the intensity function based censored or truncated data. Our results are more generious, however the assumptions we make are weak comparing with those of Ramlau-Hansen 7 and Uzuno7#7713;ullri and Wang 10. Subsequently, we use the counting process method to get the asymptotic normality of kernel estimates for the density function under mild conditions.