A synchronous motor, constructed by modifying an induction motor by fitting a permanent magnet inside the squirrel-cage rotor, is very useful for drives where synchronous operation is required or where the drop in speed of an induction motor is too great. The paper presents a theory of operation of this type of motor and suggests an empirical design method. The analysis is based on the 2-axis theory of the salient-pole synchronous motor and shows how the properties of the permanent magnet can be taken into account. The principal difficulty in designing the motor arises from the demagnetizing effect on the magnet of the heavy currents which flow when the motor is started up and synchronized. The analysis consists of two parts. First, the performance characteristics are related to the direct-axis and quadrature-axis characteristics, which show separately the variation of flux and magnetomotive force on each axis. A method is then developed for calculating the axis characteristics from the B/H curve of the permanent magnet and the dimensions of the machine. In this way the performance can be predetermined. The method is verified by tests on an existing machine. Finally, two other designs, which could be expected to give improved performance, have been worked out.