Considering motional effects in the steady-state finite-element simulation of single-phase induction machines inevitably requires a transient approach. The resulting computation time seriously hampers the application of finite elements within technical designs. In this paper, time-harmonic finite-element simulation, as commonly applied to the three-phase induction machine model, is also enabled for single-phase motors by decomposing the air-gap field in two revolving fields in the opposite direction. The advantages and drawbacks of the novel approach are illustrated by a benchmark model. Issues such as ferromagnetic saturation, external circuit coupling, adaptive mesh refinement, and torque computation are addressed. The method is used to simulate a capacitor start/run motor.