In this paper we shall address the oscillation control problems in certain classes of non-linear systems whose outputs are required to follow their inputs. It is assumed that the non-linear systems can be well represented by a set of state-space equations and undergo Hopf bifurcation at some particular value of their parameters or their inputs. A simple first-order output feedback controller is proposed for oscillation control in these non-linear systems. First it is shown that in most cases the first-order controller is effective in locally stabilizing a second-order non-linear system which is undergoing Hopf bifurcation. Then a state separation method based on the solution of the associated Riccati equation is applied to the oscillation control of higher-order non-linear systems and a second-order approximated model is developed for the purpose of designing an oscillation controller. The closed-loop stability of the reduced-order model based design is analysed and some sufficient stability conditions are provided. Finally, a detailed application example of a stepper motor is given to show how the controller design method developed in this paper is applied to practical oscillation control problems.