Wind turbines are a promising source of renewable energy. Due to the energy-intensive nature of our daily activities, reducing operating and maintenance costs is priorities in wind turbine operation. In fact, Wind Turbine Gearboxes (WTG) often operate under variable load and speed conditions, where there are problems with component frequency identification and fault diagnosis. The objective of this paper is to study the aerodynamic effects on the dynamic behaviour of WTG with the aim of providing a useful tool for designers and maintenance teams in the wind turbine industry. A dynamic model of a WTG is proposed. This gearbox consists of a planetary gear connected to the blade by an elastic coupling and a two-stage spur gear driving the generator. The aerodynamic torque is induced as an external force in the equations of motion, which are calculated using the Newmark algorithm. In addition, the stiffness of the gear mesh, which models the contact between the teeth in all wind turbine gearboxes, is sensitive to the speed variation of the rotor, which depends on the wind behaviour. The numerical results are shown in the time-domain and in the time-frequency domain as wind turbines operate in non-stationary conditions.