AbstractTWo separate models are studied for the tool tip motions during a typical machining process. One of the model is nonlinear with respect to the state variables, and the other is linear but contaminated with a time-delay effect (i.e. a differential-difference equation). First, a comparison is made between the characteristic response of these two models. Starting from the disturbed initial conditions, both models showed“oscillation damping”characteristics. Second, the question of stability is addressed, particularly for the linear time-delayed model. Two different approaches are presented: frequency domain analysis and an abstract mathematical technique. An assessment of the tolerable limitations of the imposed time lag is also conducted.