We determined coefficient of performance efficiency for the multistage toothed differentials in a device for speed change when the drive link is a sun cogwheel of the first stage, the driven link is a carrier, or vice versa, with the epicycles of separate stages as control links.Analytical dependences for determining performance efficiency of the multistage toothed differentials were derived using a method of potential power, which is the product of circular force on teeth and circular velocity of the point of initial circle of the satellite relative to the carrier, or the product of torque of a given force by angular velocity. Given the complexity of the task, we performed here a theoretical-computer study into performance efficiency of multistage toothed differentials in the devices for speed change with hydraulic systems using two- and three-stage transmissions as examples. By using a given procedure, it is possible to determine performance efficiency of the four- and multistage transmissions.We constructed graphical dependences for performance efficiency of two- and three-stage transmissions. These charts enable visual tracking of change in the value of performance efficiency depending on angular velocity of the epicycle, transfer ratio, and the number of stages.It was established that for the two- and three-stage toothed differentials the condition of automatic braking is not applicable because performance efficiency is far greater than zero. In all cases, an increase in the number of stages in toothed differential results in the decrease of performance efficiency, which confirms general patterns.The results obtained might have practical application at the stage of development and design of new devices for speed control, they make it possible to estimate operation of multi-stage toothed differentials in terms of energy consumption and automatic braking, thereby creating a basis for further research ; Определен коэффициент полезного действия дифференциалов, когда ведущим звеном является солнечное колесо первой ступени, ведомым – водило последней, а звеньями управления – эпициклы отдельных ступеней. Полученные результаты имеют практическое применение при проектировании новых устройств управления скоростью, позволяют оценить работу дифференциалов с точки зрения самоторможения и являются подспорьем для дальнейших исследований ; Визначений коефіцієнт корисної дії диференціалів, коли ведучою ланкою є сонячне колесо першої ступені, веденою – водило останньої, а ланками керування є епіцикли окремих ступеней. Отримані результати мають практичне застосування при проектуванні нових пристроїв керування швидкістю, дозволяють оцінити роботу диференціалів з огляду на енерговитрати і самогальмування та є підґрунтям для подальших досліджень