In this paper, we consider the problem of estimating the intensity of a recurrent event process observed under a standard censoring scheme. We first propose a collection of kernel estimators for which we provide MSE and MISE bounds. Then, we describe and study an adaptive procedure of bandwidth selection, in the spirit of Goldenshluger and Lepski~(2010) and we prove an oracle type bound for both the MSE and the MISE of the final estimator. The method is illustrated by simulation experiments.