It is commonplace to have multiple behaviour models that describe the same system but have been produced by different stakeholders or synthesized from different sources. Although in practice, such models frequently exhibit inconsistencies, there is a lack of tool support for analyzing them. There are two key difficulties in explaining why two behavioural models are inconsistent: (1) explanations often require branching structures rather than linear traces, or scenarios; and (2) there can be multiple sources of inconsistency and many different ways of explaining each one. In this paper, we present an approach that supports exploration of inconsistencies between modal transition systems, an extension to labelled transition systems. We show how to produce sound graphical explanations for inconsistencies, how to compactly represent all possible explanations in a composition of the models being compared, and how modelers can use this composition to explore the explanations encoded therein.