This paper addresses the control design problem for a certain class of continuous-time nonlinear systems Subject to actuator saturations. The system under consideration consists of a system with two nested nonlinearities of different type: saturation nonlinearity and cone-bounded nonlinearity. The control law investigated for stabilization purposes depends on both the state and the cone-bounded nonlinearity. Constructive conditions based on LMIs are then provided to ensure the regional or global stability of the system. Different points, like other approaches issued from the literature. are quickly discussed. An illustrative example allows to show the interest of the approach proposed. (C) 2008 Elsevier Ltd. All rights reserved.