This paper presents a quasi-three-dimensional (3-D) nonlinear magnetic equivalent circuit (MEC) model for double-sided axial flux permanent magnet machines (AFPMMs) with fractional slot concentrated windings. The proposed model can take into account not only the local magnetic saturation effect but also the 3-D flux distribution. A coupled variable permeance element is proposed in airgap modeling that captures both axial and circumferential airgap flux densities. With the help of the coupled variable permeance element, the transient magnetic field is considered by the time varying connection of the airgap and the rotor. The proposed model can be used to predict the performance of AFPMMs, including the 3-D distribution of no-load and armature airgap flux densities, no-load back electromotive force, and electromagnetic torque. In order to verify the reliability of the MEC model, two AFPMM prototypes are taken as examples, and the accuracy is verified by comparing the calculated parameters of the MEC model with the finite element analysis and experimental results. Finally, the effect of local saturation on the performances of AFPMMs is investigated.