Tailless flapping wing micro aerial vehicles (FMWAVs) are known for their light weight and agility. However, given the fact that these FWMAVs have been developed only recently, their flight dynamics have not yet been fully explained. In this paper we develop grey-box models for the time-averaged longitudinal dynamics of a tailless FWMAV (DelFly Nimble) from free-flight data using closed-loop system identification techniques. The consequence of the tailless configuration is inherent instability, therefore tailless FWMAVs are generally more complex than their tailed counterparts and require an active feedback control system. The control system introduces additional challenges to the system identification process as it counteracts the perturbations required to excite the system. Based on this approach, grey-box models were estimated and validated for airspeeds ranging from hover conditions, 0 m/s, to 1.0 m/s forward flight. Despite the complexity of the system, we were able to obtain low-order local models that are both efficient and accurate (R2 values up to 0.92) and can therefore be used for stability analysis, simulation and control design. With these models we can also take the first steps towards fully understanding the flight dynamics of tailless FWMAVs.