[en] A framework is developed for studying the implementation process, as a stepwise process in which an abstract specification is successively transformed to reach a final compilable specification adapted to the computer environment. In this context, an implementation relation is referred to as the relation which should link any ``valid'' implementation to its abstract formal specification. In other words, the implementation relation is intended to express formally the notion of validity. Our framework allows the exact characterization of the transformations which may take place at each step for a given implementation relation. This framework is essential for dealing with non-transitive implementation relations. In the second part of the paper, these results are exemplified in LOTOS on some existing relations, and an apparent paradox is presented. Some new results about these relations are also derived.