This paper presents a theoretical study of the dynamic behaviour of a wind turbine consisting of a wind rotor, a speed increaser with fixed axes, and a counter-rotating electric generator, operating in variable wind conditions. In the first part, the dynamic analytical model of the wind turbine mechanical system is elaborated based on the dynamic equations associated with the component rigid bodies and the linear mechanical characteristics associated with the direct current (DC) generator and wind rotor. The paper proposes a method for identifying the coefficients of the wind rotor mechanical characteristics depending on the wind speed. The numerical simulations performed in Simulink-MATLAB by MathWorks on a case study of a 10 kW wind turbine highlight the variation with the time of the kinematic parameters (angular speeds and accelerations), torques and powers for wind system shafts, as well as the mechanical efficiency, both in transient and steady-state regimes, considering variable wind speed. The analytical and numerical results are helpful for researchers, designers, developers, and practitioners of wind turbines aiming to optimise their construction and functionality through virtual prototyping.