Dynamic stability of a flexible cam-follower is considered. The shaft-cam-follower assembly is modeled by a single degree of freedom system. In the analysis, transverse and rotational flexibilities of the camshaft along with flexibility of the follower are taken into consideration. This gives rise to a system governed by a linear, second-order, ordinary differential equation with time-dependent coefficients. In general, this class of equations is known as second order Hill’s equation. The time responses of the cam-follower system for an eccentric cam under different rotational speeds are determined. In addition, the stability analysis based on Hill’s infinite determinant is performed, and the effects of operational speed and damping on the stability are determined. For the special case of the cam-follower system that has been considered, it has been found that the system is stable for lower values of the angular speed of the cam. As the speed is increased gradually, a few unstable regions occur. In general, damping shows a significant effect on stabilizing the cam-follower system.