This paper deals with dynamic models for three-phase bearingless flux-switching permanent-magnet (FSPM) linear machines. This machine type can be used to build a magnetically levitating long-range linear drive system, whose rail does not need any active materials apart from iron. A dynamic machine model is developed by means of equivalent magnetic models, taking into account air-gap variation and magnetic saturation. The effects of these phenomena are analyzed using finite-element method (FEM) simulations of a test machine. The parameters of the proposed model can be identified using the FEM or measured data. The model can be applied to real-time control and time-domain simulations. The model is validated by means of experiments.