We address the problem of transferring semantic annotations to new languages using parallel corpora. Previous work has transferred these annotations on a token-to-token basis, an approach that is sensitive to alignment errors and translation shifts. We present a global approach to transfer that aggregates information across the whole parallel corpus and leads to more robust labellers. We build two global models, one for predicate labelling and one for role labelling, each tailored to the task at hand. We show that the combination of direct and global methods outperforms previous results.