This is a revised and extended version of the paper "Approximate-based Multi-Modal Systems and Possibilistic Logic: A comparative study" in proc. of ESTYLF'96, Publi. Univ. Oviedo (Spain), pp. 113-118.The paper introduces a general axiomatic notion of approximation mapping, a mapping that associates to each crisp proposition p a fuzzy set representing approximately p. It is shown how it can be obtained through fuzzy relations, which are at least reflexive. We study the corresponding multi-modal systems depending on the properties satisfied by the approximate relation. Finally, we show some equivalences between possibilistic logical consequences and global/local logical consequences in the multi-modal systems.This research has been partially supported by the CSIC-CNRS grant called "Similarity-based reasoning and its applications" and by the CICYT, TIC96-1138-C04-01 project SMASH.Peer reviewed