Japanese case markers, which indicate the grammatical relation of the complement NP to the predicate, often pose challenges to the generation of Japanese text, be it done by a foreign language learner, or by a machine translation (MT) system. In this paper, we describe the task of predicting Japanese case markers and propose machine learning methods for solving it in two settings: (i) monolingual, when given information only from the Japanese sentence; and (ii) bilingual, when also given information from a corresponding English source sentence in an MT context. We formulate the task after the well-studied task of English semantic role labelling, and explore features from a syntactic dependency structure of the sentence. For the monolingual task, we evaluated our models on the Kyoto Corpus and achieved over 84% accuracy in assigning correct case markers for each phrase. For the bilingual task, we achieved an accuracy of 92% per phrase using a bilingual dataset from a technical domain. We show that in both settings, features that exploit dependency information, whether derived from gold-standard annotations or automatically assigned, contribute significantly to the prediction of case markers.