We investigate the problem of synchronizing nonidentical or perturbed nonlinear systems. In the considered setup, the systems are incapable to synchronize under diffusive couplings. Instead, assuming the QUAD property for each system, we derive conditions under which the synchronization error can be kept arbitrarily small by a proper choice of the interconnection structure. This motivates the definition of practical synchronization as an alternative synchronization notion for nonidentical or perturbed dynamical systems. The presented results are intimately related to synchronization of passive systems, but it is shown that the stronger QUAD assumption is essential in our framework. The proposed concept of practical synchronization translates directly into a notion of robust synchronization. Beyond that, the results open the way for an investigation of synchronization phenomena on unbalanced graphs, leading to the concept of cluster synchronization. (C) 2014 Elsevier Ltd. All rights reserved.