Abstract: In many biomedical and engineering studies, recurrent event data and gap times between successive events are common and often more than one type of recurrent events is of interest. It is well known that the proportional hazards model may not be appropriate for fitting survival times in some settings. In the paper, we consider an additive hazards model for multiple type recurrent gap times data to assess the effect of covariates. For inferences about regression coefficients and baseline cumulative hazard functions, an estimating equation approach is developed. Furthermore, we establish asymptotic properties of the proposed estimators.