A problem of adaptive control methods application to a speed vector control system of a Permanent Magnet Synchronous Motor (PMSM) with time varying mechanical parameters is considered. Such methods analysis is made to select the most appropriate one for the problem under consideration. As a result, a neural tuner is chosen. A synchronous motor mathematical model is shown, and the vector based control system of the motor is described. The neural tuner structure and its operation principle are presented. It is applied to adjust the speed controller of the PMSM. Experiments are conducted using the mathematical model of a PMSM Siemens 1FK7103, in which the mechanical inertia moment value is changed gradually during the modeling process. The tuner application as an augmentation to the speed controller allows to keep the required transient quality during the experiment despite the drive nonstationarity in contrast to a P-controller with the constant parameter value. This results in avoidance of, firstly, the transient time increase when the inertia moment is higher than its nominal value and, secondly, the speed overshoot in vice versa case.