As subsea production of oil and gas reaches deeper and more remote waters, the need for more compact separation equipment arises. The gas liquid cylindrical cyclone (GLCC) is a widely used separation device in topside facilities, but has yet to reach the same popularity subsea. The GLCC separates gas and liquid by inducing a swirl on the multiphase flow. Because of its small size, the GLCC is sensitive to flow variations which may reduce separation performance. The performance of the GLCC can be improved by control. In this paper we consider a nonlinear dynamic model of a GLCC containing unmeasured variables and states. We present an adaptive feedback linearizing controller and prove that the origin of the gas pressure and liquid level error systems are locally asymptotically stable in the sense of Lyapunov on a specified domain. The model and controller are implemented in Simulink and simulations show that the controller works very well, even with uncertainties in assumed known parameters, and measurement noise.