An adaptive master-slave output feedback synchronization problem is studied firstly for a network of interconnected nonlinear dynamical systems with bounded disturbance and then for a network of systems with delayed couplings. The proposed structure of decentralized controller and adaptation algorithms in both cases is based on speed-gradient and passification methods. Synchronization conditions for systems with disturbances and for systems with delayed couplings are established. An example of synchronization of the network of Chua systems with bounded disturbances is given. The problem of convergence with prespecified accuracy is examined for the networks of dynamical systems with disturbances. (1)