Recent research has indicated that the permanent magnet motor drives which include the permanent magnet synchronous motor (PMSM) and the brushless DC motor (BDCM) could become serious competitors to the induction motor for servo applications. The PMSM has a sinusoidal back emf and requires sinusoidal stator currents to produce constant torque while the BDCM has a trapezoidal back emf and requires rectangular stator currents to produce constant torque. The PMSM is very similar to the wound rotor synchronous machine except that the PMSM that is used for servo applications tend not to have any damper windings and excitation is provided by a permanent magnet instead of a field winding. Hence the d,q model of the PMSM can be derived from the well known model of the synchronous machine with the equations of the damper windings and field current dynamics removed. Because of the nonsinusoidal variation of the mutual inductances between the stator and rotor in the BDCM, it is also shown in this paper that no particular advantage exists in transforming the abc equations of the BCDM to the d,q frame. Hence the solution of the original abc equations is proposed for the BDCM.