Multi-Context Systems (MCSs) introduced by Brewka and Eiter are a promising way to interlink decentralized and heterogeneous knowledge contexts. In this paper, we propose Preferential Multi-Context Systems (PMCSs), which provide a framework for incorporating preference over contexts in MCSs. In such a PMCS, its contexts are divided into different strata according to the preference such that information flows only from a context to contexts in the same stratum or less preferred strata. Given a positive integer l, the first l preferred strata of a PMCS are able to fully capture information exchange between the contexts of these strata, and thus these contexts form a new PMCS called the l-section of the original PMCS. We generalize the equilibrium semantics for an MCS to l(<=)-equilibria for a PMCS. An l(<=)-equilibrium represents a belief state that is acceptable at least for the l-section of the given PMCS. We also investigate inconsistency analysis in PMCS and related computational complexity issues. (C) 2016 Elsevier Inc. All rights reserved.