Abstract: Researchers usually use linear models for the study of vibrations because they are simpler for the analysis. Practice shows that these models do not fully characterize real processes. This is the case in machining processes, where linear models cannot characterize the instability of the processing or even the chaotic motions of the technological system. The model presented in the paper has four degrees of freedom and is a nonlinear one. The nonlinearity is given by the expression of the cutting force as a function of the cutting depth. The loss of contact between the tool and the workpiece is not considered; in other words, the vibration amplitudes are small enough for this phenomenon not to occur. Nonlinear vibrations are obtained, for which a numerical characterization is performed. The paper also contains a numerical example illustrating the theory.