We propose a multibody model of a freewing UAV. This model allows obtaining simulations of the UAV's behaviour and, in the future, to design a control law stabilising the entire flight envelope (hovering and forward flight). We also describe the realisation of a prototype and a comparison of possible methods for estimating the UAV's states. With this prototype, we report on experimental hovering flights with a non-linear incremental dynamic inversion controller to stabilise the wing and a proportional derivative controller for the fuselage stabilization.