This chapter considers a one-degree-of-freedom system with linear elastic force characteristics and linear damping. It discusses a simple algorithm for describing a flexible clutch system with non-linear characteristics. In multi-degrees-of-freedom non-linear vibrating systems one finds it difficult to damp effectively the vibration close to sub harmonic, super harmonic or combined resonances. This problem is important, from the practical point of view, since real systems often exhibit non-linearities due to geometry and rheology. The condition for elimination of the non-harmonic resonance was brought to a simple relationship between the coefficients describing the non-linear terms of the spring characteristics. It seems to be convenient, the more so as a limitation of resonant amplitudes can be achieved by changing proportions between non-linear characteristics without changing other system parameters.