Reluctance synchronous machines (RSMs) are characterized by high nonlinearities, cross-coupling effects and high torque ripple. This paper presents a nonlinear machine model of three-phase RSMs based on a nonlinear electromagnetic model including iron losses and a novel (extended) torque equation. The γ-component is used to consider asymmetries. The novel torque model provides a precise approximation of the machine’s torque ripple. Iron losses are covered as well. The nonlinear machine model with extended torque equation is implemented based on current, angle and speed dependent flux linkage and iron loss maps. Finally, the nonlinear and extended machine model is validated by comparing with state-of-the-art results obtained by finite-element analysis (FEA).