Requirements elicitation involves the construction of large sets of conceptual models. An important step in the analysis of these models is checking their consistency. Existing research largely focuses on checking consistency of individual models and of relationships between pairs of models. However, such strategy does not guarantee global consistency. In this paper, we propose a consistency checking approach that addresses this problem for homogeneous models. Given a set of models and a set of relationships between them, our approach works by first constructing a merged model and then verifying this model against the consistency constraints of interest. By keeping proper traceability information, consistency diagnostics obtained over the merge are projected back to the original models and their relationships. The paper also presents a set of reusable expressions for defining consistency constraints in conceptual modelling. We demonstrate the use of the developed expressions in the ...