This paper investigates the principles underlying torque production in a flux-switching permanent magnet (FSPM) machine. Because the phase windings and permanent magnets in FSPM machines are both located on the stator, the torque production mechanism is not the same as for a conventional PM synchronous machine. Spatial harmonic analysis is applied to examine the frequency components present in the electric loading and magnetic loading of the machine. Since torque is proportional to the product of the electric and magnetic loading, understanding the source of the principal harmonics in these waveforms yields powerful insights into the components that result in torque production. The analysis is first presented for a specific FSPM machine (12-slot, 10-pole) and then extended to a general FSPM machine. The primary torque-producing harmonics in the airgap flux density waveform are found to be the heterodyned harmonics of the MMF produced by the stator magnets and the airgap permeance seen by the stator looking into the rotor. Analytical results are compared to results from finite element (FE) analysis and exhibit good agreement.