Nonparametric kernel estimators for hazard functions and their derivatives are considered under the random left truncation model. The estimator is of the form of sum of identically distributed but dependent random variables. Exact and asymptotic expressions for the biases and variances of the estimators are derived. Mean square consistency and local asymptotic normality of the estimators are established. Adaptive local bandwidths are obtained by estimating the optimal bandwidths consistently. © 1993 The Institute of Statistical Mathematics.