A new form of linear hybrid synchronous motor is described; it has a polyphase primary winding with surface-mounted permanent magnets and a simple passive segmental secondary. The number of permanent magnets in one wavelength of the primary winding determines the number of segments and the gear ratio, which is the ratio of secondary speed to primary travelling field speed; a gear ratio of 5 gives a particularly low force ripple. If the secondary is laminated, the machine can operate with high efficiency and a power factor close to unity. A double-sided form of the machine cancels the normal force on the secondary and has a better performance than the single-sided form. The machine is accurately represented by a simple equivalent circuit, with parameters that can be determined from two finite-element solutions corresponding to open-circuit and short-circuit tests. Finite-element results for the performance of example single-sided and double-sided designs are presented, showing the effects of varying the supply voltage, supply frequency, magnet depth and secondary material. Tractive force values predicted by finite-element analysis have been confirmed by static measurements in an experimental machine.