Interlinking knowledge sources to enable information exchange is basic means to build enriched knowledge-based systems, which gains importance with the spread of the Internet. Inconsistency, however, arises easily in such systems, which is not least due to their heterogeneity, but also due to their independent design. This makes developing methods for consistency management of such systems a pressing issue. An important aspect is that in many relevant cases, the information at individual sources may not be amenable to change in order to resolve inconsistency, like in case of autonomous management of the sources. We thus aim at analyzing inconsistency of a system by means of the interlinking of sources and changes thereof. More concretely, we consider the powerful framework of Multi-Context Systems, in which decentralized and heterogeneous system parts interact via (possibly nonmonotonic) bridge rules for information exchange. Nonmonotonicity and potential cyclic dependencies pose additional challenges that call for suitable methods of inconsistency analysis. We thus provide two approaches for explaining inconsistency, which both characterize inconsistency in terms of bridge rules, but in different ways: by pointing out rules which need to be altered for restoring consistency, and by finding combinations of rules which cause inconsistency. We show duality and modularity properties of these notions, give precise complexity characterizations, and provide algorithms for their computation, which have been implemented in a prototype, by means of so-called Hex-programs. Our results provide a basis for inconsistency management in heterogeneous knowledge systems which, different from and orthogonal to other works, explicitly addresses the knowledge interlinks in order to restore consistency. (C) 2014 Elsevier B.V. All rights reserved.