Abstract Lexical cohesion arises from a chain of lexical items that establish links between sentences in a text. In this paper we propose three different models to capture lexical cohesion for document-level machine translation: (a) a direct reward model where translation hypotheses are rewarded whenever lexical cohesion devices occur in them, (b) a conditional probability model where the appropriateness of using lexical cohesion devices is measured, and (c) a mutual information trigger model where a lexical cohesion relation is considered as a trigger pair and the strength of the association between the trigger and the triggered item is estimated by mutual information. We integrate the three models into hierarchical phrase-based machine translation and evaluate their effectiveness on the NIST Chinese-English translation tasks with large-scale training data. Experiment results show that all three models can achieve substantial improvements over the baseline and that the mutual information trigger model performs better than the others.