A concept of dynamic stability of quasi-static paths is proposed that takes into account the existence of fast (dynamic) and slow (quasi-static) time scales. A change of variables is performed that replaces the (fast) physical time $t$ by a (slow) loading parameter $\lambda$, whose rate of change with respect to time, $\epsilon=d\lamda/dt$, is decreased to zero. This leads to a system of dynamic equations defining a singular perturbation problem: the highest order derivative with respect to $\lambda$ appears multiplied by $\epsilon$. The proposed definition is essentially a continuity property with respect to the smallness of initial perturbations (as in Lyapunov stability) and loading rate $\epsilon$ (as in singular perturbation problems). Three mechanical examples (the Ziegler and Shanley columns and a pin-on-flat friction apparatus) are presented to illustrate similarities and differences between ?dynamic stability of quasi-static paths? and Lyapunov stability of some related equilibrium configurations or dynamic trajectories.