This paper is concerned with the analysis of the synchronization of networks of nonlinear oscillators through an innovative local adaptive approach. In particular, time-varying feedback coupling gains are considered, whose gradient is a function of the local synchronization error over each edge in the network. It is shown that, under appropriate conditions, the strategy is indeed successful in guaranteeing the achievement of a common synchronous evolution for all oscillators in the network. The theoretical derivation is complemented by its validation on a set of representative examples. (C) 2009 Elsevier Ltd. All rights reserved.