The topic of the article is construction and study of the closed mathematical model of a dual-propeller horizontal axis wind turbine (HAWT). One propeller is rigidly connected to the carrier of a differential planetary gear (DPG), the other propeller is rigidly joined to the external gear of the DPG, the rotor of the generator is rigidly joined to the sun gear. The generator is connected to a local electric circuit. The external resistance in the circuit is a varied parameter of the model. The aerodynamic forces acting upon the propellers are modeled using a quasi-steady approach. The electromagnetic torque acting upon the rotor of the generator is supposed to be a linear function of the angular speed of this rotor. Equations of the steady motions of a HAWT are derived. The optimal value of a gear ratio is calculated depending on the aerodynamic characteristics of the propellers. The external resistance, for which the mechanical power of the turbine is close to its maximum, is found. The operating modes for this external resistance and their domains of attraction are described. A possibility of acceleration of one propeller by means of the other propeller is discussed. The control strategy, which transfers the system to the program operating mode, is constructed. Two types of control are used: variation of the external resistance in the local circuit of the generator and application of a brake to one of the rings of the DPG.