Steady-state operation modes of three-phase induction machines can be efficiently simulated by 2D nonlinear time-harmonic finite-element models, although only induced currents with respect to the fundamental air-gap field are correctly taken into account. This technique does not generalise to single-phase induction machines. An approach based on multiple rotor models and a spectral decomposition of the air-gap field enables to consider higher harmonic air-gap field contributions. In a capacitor-motor model, the first, third and fifth forward and backward rotating components give raise to different frequencies in the rotor which result in different eddy-current effects. The torque dip due to the third harmonic is accurately simulated.