The stability of machine tool systems is analyzed by considering the machining process as a stochastic process without decomposing into machine tool structural dynamics and cutting processes. In doing so the time series analysis technique developed by Wu and Pandit is applied systematically to the relative vibration between cutting tool and work- piece measured under actual working conditions. Various characteristic properties derived from the fitted ARMA(Autoregressive Moving Average) Models and those from raw data directly are investigated in relation with the system stability. Both damping ratio and absolute value of the characteristic roots of the AR part of the most significant dynamic mode are preferred as stability indicating factors to the other pro-perties such as theoretical variance .gamma. (o) or absolute power of the most dominant dynamic mode. Maximum aplitude during a certain interval and variance estimated from raw data are shown to be very sensi- tive to the type of the signal and the location of measurement point although they can be obtained rather easily. The relative vibration signal is also analyzed by FFT(Fast Fourier Transform) Analyzer for the purpose of comparison with the spectrums derived from the fitted ARMA models.