Purpose. Obtaining analytical dependencies for calculating the optimum speedup and speeddown times for a frequencycontrolled asynchronous motor that minimize the main electromagnetic energy losses of the engine for small displacements of its shaft, and also the estimation of the influence of these optimal speedup and speeddown times on the value of the main electromagnetic energy losses in the frequency-controlled asynchronous motor various types of engine tachograms (with linear and parabolic forms or hyperbolic sine form).Methodology. Methods of optimal control and simulation modelling.Findings. Analytical dependencies are obtained and a graphoanalytical method proposed for calculating the optimum speedup and speedown times for the frequency-controlled asynchronous motor that minimizes the main electromagnetic energy losses of the motor with small displacements of its shaft. The effect of these optimal speedup and speeddown times on the value of the main electromagnetic energy losses in the frequency-controlled asynchronous motor under different types of motor tachograms (with linear and parabolic forms or the form of the hyperbolic sine) are estimated. Originality. For the first time, analytical dependencies are obtained for calculating the optimal speedup and spedddown times for small displacements of the frequency-controlled asynchronous motor, by which the electromagnetic losses in the motor is minimized. For the first time, a graphoanalytical method developed to determine these optimum speedup and speeddown times for the frequency-controlled asynchronous motor when was working out small displacements.Practical value. An approach to energy saving in positional frequency-controlled asynchronous electric drives is proposed, by optimizing their speedup and speeddown times, which allows in practice without significant capital costs to reduce power losses in these electric drives