<p>Ferromagnetic alloys are considered promising materials for creating highly damping coatings that help suppress resonance oscillations of elements of complex mechanical systems, such as titanium compressor blades in gas turbine engines. However, the effectiveness of such coatings depends largely on their dynamic properties. In this work, using the example of a ferromagnetic Co-Fe coating deposited on a titanium plate, frequency responses (FR) of the plate–coating system were investigated by exciting first bending mode oscillations in it. The characteristic features of the nonlinearity of this system have been established, which manifest themselves in the non-monotonic change in resonance frequency with increase in the amplitude of forced oscillations, in the presence of a “hysteresis” effect in FR profiles when changing the direction of their scanning frequency, as well as in the sharp asymmetry of their shape. At the same time, with increase in the amplitude of oscillations in the range of “small” amplitudes, the resonance frequency decreases (soft nonlinearity), and in the region of “large” amplitudes, greater than a certain critical amplitude, it increases (hard nonlinearity). The relationship between the resonance frequency and amplitude in each of these regions can be described, in the first approximation, by the Duffing model, which assumes a quadratic deviation of the restoring force from the linear dependence of the displacement of the pendulum from its equilibrium position.</p>