Abstract <p>The influence of the misalignment angle during gear engagement on the service life of a transmission, expressed by the number of loading cycles to failure of the gear wheel teeth, is investigated. An approach is proposed that makes it possible to solve the problem analytically and obtain a relationship between the misalignment angle and the number of cycles to failure. Such a relationship is derived based on the well-known empirical correlation between the level of contact stresses and the fatigue life under cyclic loading. The analytical dependences obtained can be used at the stages of design and engineering development of gear transmissions, especially in choosing the optimal engagement parameters and predicting the resource of gear systems under conditions close to real operation.</p>