This paper proposes an adaptive path-following controller of small fixed-wing Unmanned Aerial Vehicles (UAVs) in the presence of wind disturbances, which explicitly considers that wind speed is time-varying. The main idea was to formulate UAVs path-following as control design for systems with parametric uncertainties and external disturbances. Assuming that there is no prior information on wind, the proposed solution is based on the L 1 adaptive control, using linearized model dynamics.This approach makes clear statements for performance specifications of the controller and relaxes the common constant wind velocity assumption. This makes the design more realistic and the analysis more rigorous, because in practice wind is usually time varying (windshear, turbulence and gusting).The path-following controller was demonstrated in flight under wind speed up to 10m/s, representing 50% of the nominal UAV airspeed.