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This paper addresses the hybrid synchronization problem in two nonlinearly coupled complex networks with asymmetrical coupling matrices under pinning control schemes. The hybrid synchronization of two complex networks is the outer antisynchronization between the driving network and the response network while the inner complete synchronization in the driving network and the response network. We will show that only a small number of pinning feedback controllers acting on some nodes are effective for synchronization controlof the mentioned dynamical networks. Based on Lyapunov Stability Theory, some simple criteria for hybridsynchronization are derived for such dynamical networks by pinning control strategy. Numerical examplesare provided to illustrate the effectiveness of our theoretical results

Pinning Two Nonlinearly Coupled Complex Networks with an Asymmetrical Coupling Matrix