For a network of interconnected nonlinear dynamical systems an adaptive leader-follower output feedback synchronization problem is considered. The proposed structure of decentralized controller and adaptation algorithm is based on speed-gradient and passivity. Sufficient conditions of synchronization for one class of heterogeneous networks are established. An example of synchronization of the network of nonidentical Chua systems is analyzed. The main contribution of the paper is adaptive controller design and analysis under conditions of incomplete measurements, incomplete control and uncertainty.