This article presents statistical language translation models called "dependency transduction models'', based on collections of "head transducers''. Head transducers are middle-out finite-state transducers which translate a headword in a source string into its corresponding head in the target language, and further translate sequences of dependents of the source head into sequences of dependents of the target head. The models are intended to capture the lexical sensitivity of direct statistical translation models, while at the same time taking into account the hierarchical phrasal structure of language. Head transducers are suitable for direct recursive lexical translation, and are simple enough to be trained fully automatically. The authors present a method for fully automatic training of dependency transduction models for which the only input is transcribed and translated speech utterances. They apply the method to create English–Spanish and English–Japanese translation models for speech translation applications.