Abstract : This work deals with the Hybrid Excitation Synchronous Machines (HEMS) study and the Permanent Magnets Synchronous Machines (PMSM) design for hybrid vehicles applications in order to reduce the vehicles polluting emission reduction. The hybrid vehicle, associated with PMSM and HEMS constitutes from this point of view an interesting solution to solve these problems. Several PMSM analytical electromagnetic models (linear or not) based on the Park transformation and the use of reluctant networks were developed. Those make it possible to combine precision, fast computations and simplicity. A HEMS was designed and achieved at SATIE laboratory and answered a specification sheet of hybrid vehicle provided by PSA group. This one could answer the constraints of the specifications at the same time in term of sizing and performances.