This paper investigates the hybrid chaos synchronization of identical 4-D hyperchaotic Liu systems (2006), 4-D identical hyperchaotic Chen systems (2005) and hybrid synchronization of 4-D hyperchaotic Liu and hyperchaotic Chen systems. The hyperchaotic Liu system (Wang and Liu, 2005) and hyperchaotic Chen system (Li, Tang and Chen, 2006) are important models of new hyperchaotic systems. Hybrid synchronization of the 4-dimensional hyperchaotic systems addressed in this paper is achieved through complete synchronization of two pairs of states and anti-synchronization of the other two pairs of states of the underlying systems. Active nonlinear control is the method used for the hybrid synchronization of identical and different hyperchaotic Liu and hyperchaotic Chen and the stability results have been established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the proposed nonlinear control method is effective and convenient to achieve hybrid synchronization of the hyperchaotic Liu and hyperchaotic Chen systems. Numerical simulations are shown to demonstrate the effectiveness of the proposed chaos synchronization schemes.