Statistical machine translation systems are usually trained on large amounts of bilingual text (used to learn a translation model), and also large amounts of monolingual text in the target language (used to train a language model). In this article we explore the use of semi-supervised model adaptation methods for the effective use of monolingual data from the source language in order to improve translation quality. We propose several algorithms with this aim, and present the strengths and weaknesses of each one. We present detailed experimental evaluations on the French–English EuroParl data set and on data from the NIST Chinese– English large-data track. We show a significant improvement in translation quality on both tasks.