An unsolved problem in the analysis of capture-recapture experiments is the estimation of the size of an open population when the capture probabilities are heterogeneous across the population. Here, we extend a kernel smoothing approach of Huggins and Yip (Biometrics 55 (1999) 387) to the martingale estimating functions based on sample coverage of Chao et al. (J. Statist. Plann. Inference 92 (2001) 213) and solve this problem when there are frequent capture occasions. Simulation results are shown to examine the performance of the proposed estimation procedure. A real data set is used for illustration. (C) 2002 Elsevier Science B.V. All rights reserved.