In the paper the mathematical model of the drive system of a brushless motor with permanent magnet excitation PMSM is presented. The mathematical analysis of drive systems is a complex task. The mathematical model covers a brushless motor with permanent magnet excitation, supplied from a three-phase sine waveform current source. The load is also included in the load. In the paper the time dependencies of motor currents, electromagnetic moment and velocities are presented. These dependencies make it possibile to analyze the dynamical processes occurring in the considered drive system. The results have been presented in the form of charts.