Abstract:  This article addresses the oscillation control problems in certain classes on nonlinear systems. It is assumed that the nonlinear systems can be well represented by a set of state space equations and that undergo Hopf bifurcation at some particular value of their parameters or their inputs.  A simple first order output feedback control is proposed for oscillation control in these nonlinear systems. First it is shown that in most cases the first order controller is effective in locally stabilizing a second order nonlinear system which is undergoing Hopf bifurcation. Then a state separation method based on the solution of the Riccati equation is applied to the oscillation control of higher order nonlinear 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.