The paper considers the issues of correct modelling of the dynamics of mechanical system components with elastic-damping magnetic support elements. The focus of the research is to prove the need to use nonlinear mathematical models for adequate simulation of various dynamic phenomena. As a typical example of a dynamic mechatronic system, a rotor in a full passive-active magnetic suspension with two radial passive and one axial active magnetic bearing. To describe the dynamics of model rotor, a system of nonlinear differential equations is used, obtained on basis of the Lagrange-Maxwell equations for the correct consideration of the interrelation of mechanical and electromagnetic processes. In these equations, the description of the force characteristics of radial passive magnetic bearings is performed using third-order polynomials relative to the displacement of the rotor. This corresponds to the calculated and experimental data. For the numerical analysis of this system, the Runge-Kutta method was used. In nonlinear solutions, sub- and super-harmonic responses to monoharmonic excitation from the rotor’s own imbalance and other phenomena inherent in nonlinear systems were observed. Variant studies were conducted to compare responses with these solutions when replacing nonlinear force characteristics with analogs linearized in various ways. Evaluation of the possibility of linearization for adequate assessment of the danger of various modes allowed identifying critical discrepancies also confirmed by comparison with experimental data. This fact made it possible to reasonably prove the need to use nonlinear models to describe the dynamics of complex combined systems with elastic-damping passive and active magnetic vibration-damping elements.