Today, simulation of electrical drives with asynchronous motors based on systems of differential equations is regarded as one of the principal means of their research study. The difficulty of the simulation is determined by the need for accuracy of the results obtained and the complexity of the mathematical model’s differential equations. In this article, we present a study of the particularities of the simulation of electrical drives systems with asynchronous motors. We have studied models composed of three-phase and orthogonal coordinates systems and we have shown that qualitative and quantitative differences exist in the process of changing the angular speed of the rotor and electromagnetic torque. The result obtained is above all influenced by the non-linear character of the load opposing a fan-type or “dry friction”-type resistant torque. For dual-earthed electromagnetic actuation with the moments of the resistant torques indicated, integration of differential equation systems was carried out with various digital methods used in professional mathematical software for simulation.