Lexicalized Tree Adjoining Grammar (LTAG) is an attractive formalism for linguistic description mainly because of its extended domain of locality and its factoring recursion out from the domain of local dependencies (Joshi, 1984, Kroch and Joshi, 1985, Abeillé, 1988). LTAG's extended domain of locality enables one to localize syntactic dependencies (such as filler-gap), as well as semantic dependencies (such as predicate-arguments). The aim of this paper is to show that these properties combined with the lexicalized property of LTAG are especially attractive for machine translation. The transfer between two languages, such as French and English, can be done by putting directly into correspondence large elementary universe without going through some interlingual representation and without major changes to the source and target grammars. The underlying formalism from the transfer is "synchronous Tree Adjoining Grammars" (Sheiber and Schabes [1990]). Transfer rules are stated as correspondences between nodes of trees of large domain of locality which are associated with words. We can thus define lexical transfer rules that avoid the defects of a mere word-to-word approach but still benefit from the simplicity and elegance of a lexical approach. We rely on the French and English LTAG grammars (Abeillé [1988], Abeillé [1990(b)], Abeillé et al. [1990], Abeillé and Schabes [1989, 1990]) that have been designed over the past two years jointly at University of Pennsylvania and University of Paris 7-Jussieu.