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A new nonlinear grey box (NLGB) model of switched reluctance motors (SRM) based on first modeling principles is developed. This model is obtained by representing the inductances of the machine phases by a series of functions modeling the periodic variation of the permeance of the phase magnetic circuits with respect to the rotor position, weighted each by a smooth function taking into account the flux saturation. The structure of this model is obtained by expanding the periodic behavior and saturation phenomenon as Fourier series and Legendre polynomials respectively, and its parameters are estimated from input-output data by minimizing the estimation error of the phase flux linkage given in a linear regression form with respect to the searched parameters. The consistency and accuracy of the developed NLGB model are confirmed by simulation within an automotive application.