Scalable decentralized stability certificates in networks i.e. decentralized stability guarantees for an arbitrary interconnection of heterogeneous dynamical systems, are often based on certain symmetry assumptions in the way the systems are interconnected. Such structure simplifies the mathematical analysis significantly, nevertheless a potential pitfall needs to be addressed: the stability proof might offer no robustness guarantees to deviations from protocol symmetry. This is, for example, the case for Internet congestion control stability results for arbitrary networks i.e. the stability proofs break down with an arbitrarily small deviation from protocol symmetry. We propose in the paper conditions that can guarantee scalable robust stability in a nonsymmetric interconnection setting for a class of networks that includes Internet congestion control models and consensus protocols. The certificates derived are decentralized and scale with the degree of nonsymmetry. (C) 2007 Elsevier Ltd. All rights reserved.