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In the last years, statistical machine translation has already demonstrated its usefulness within a wide variety of translation applications. In this line, phrase-based alignment models have become the reference to follow in order to build competitive systems. Finite state models are always an interesting framework because there are well-known efficient algorithms for their representation and manipulation. This document is a contribution to the evolution of finite state models towards a phrase-based approach. The inference of stochastic transducers that are based on bilingual phrases is carefully analysed from a finite state point of view. Indeed, the algorithmic phenomena that have to be taken into account in order to deal with such phrase-based finite state models when in decoding time are also in-depth detailed.