The generalized synchronization of hyperchaos systems is investigated. Based on the Lyapunov stability theory, a new linear and nonlinear generalized synchronization approach is proposed. Theoretical analysis is provided to show its feasibility. The proposed method can realize the generalized synchronization not only of structurally equivalent systems, but also of systems of different dimensions. If the error gain matrix is suitably chosen, the generalized synchronization between drive system and response system will be obtained. Numerical simulations further demonstrate the effectiveness of the proposed scheme.