Tailless flapping wing micro aerial vehicles (FMWAV) are known for their light weight and agility. However, given the fact that these FWMAVs have been recently developed, their flight dynamics have not yet been fully explained. In this paper we will develop local time-averaged longitudinal grey-box models based on closed-loop system identification techniques, where free-flight experimental data, obtained from the DelFly Nimble, is used to estimate and validate the local grey-box models. With these models we can take the first steps towards fully understanding the flight dynamics of tailless FWMAVs. The consequence of the tailless configuration is inherent instability and therefore tailless FWMAVs are generally more complex, compared to its tailed counterpart, and require a active feedback control system. The active feedback control system introduces additional challenges to the system identification process since it follows that feedback control works against the objectives of system identification. Dynamic effects that play a major role when studying the dynamic behaviour of FWMAVs are the sub-flap and the flap cycle-averaged effects. However, in this paper, we are only interested in modelling the flap cycle-averaged (time-averaged) effects of the DelFly Nimble. Based on this approach, grey-box models were estimated and validated for airspeeds near hover condition 0 m/s, up 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) to predict the flight dynamic behaviour of the DelFly Nimble and can therefore be used for stability analysis, simulation and control design.