Summary Recurrent events data are commonly seen in longitudinal follow-up studies. Dependent censoring often occurs due to death or exclusion from the study related to the disease process. In this article, we assume flexible marginal regression models on the recurrence process and the dependent censoring time without specifying their dependence structure. The proposed model generalizes the approach by Ghosh and Lin (2003, Biometrics 59, 877–885). The technique of artificial censoring provides a way to maintain the homogeneity of the hypothetical error variables under dependent censoring. Here we propose to apply this technique to two Gehan-type statistics. One considers only order information for pairs whereas the other utilizes additional information of observed censoring times available for recurrence data. A model-checking procedure is also proposed to assess the adequacy of the fitted model. The proposed estimators have good asymptotic properties. Their finite-sample performances are examined via simulations. Finally, the proposed methods are applied to analyze the AIDS linked to the intravenous experiences cohort data.