The synchronization process of three-phase line start permanent magnet synchronous motors (LSPM) with buried magnets and a squirrel-cage is studied in this paper. The goal is to define a pull-in criterion by using a Lyapunov function. A model is first derived and a Lyapunov function is defined using the Lagrange-Charpit method. Experiments and simulations are then compared to check the validity of the model. A criterion to define the capability of synchronization of LSPM motors is then presented. This criterion is used to study the influence of the electrical parameters on the synchronization capability of two four pole LSPM motors. The first experiments proved that the prototypes have greater synchronization capability than the criterion predicts