In this article we describe the statistical approach to machine translation as implemented in the stattrans module of the Verbmobil system. The statistical translation approach uses two types of information: a translation model and a language model. The language model used is an m-gram model. The translation model comprises a stochastic lexicon and word position parameters. To capture dependencies between word groups in each of the two languages, alignment templates are used. We describe the components of the system and report results on the Verbmobil task. The experience obtained in the Verbmobil project shows that the statistical approach is very competitive with other translation approaches.