Abstract: Vibrations of the wheel head of a universal cylindrical grinding machine was analysed and the results obtained by two methods - the method of real-mode analysis and that of complex-mode analysis were compared. The analyses show that for systems of few-degrees-of-freedom, there is little difference between the results of the above two methods. Since the real-mode analysis method is much simpler than the complex-mode analysis method, it is preferable to use the real-mode analysis method for systems of few-degrees-of-freedom.