This document presents, in a first stage, a synthetic description of the implementation of the concept of local mechanical, or "microscopic", approach proposed by Institut de Soudure for predicting the fatigue damage to fillet welded assemblies as a function of the weld geometry. In a second stage, a re-definition of the local endurance criterion is proposed in order to integrate the incidence of the residual stresses inherent in the welding process. The numerical simulation of welding, by using the SYSWELD calculation code, represents a decisive choice for predicting in each susceptible zone (toe and root) of the weld the complete tensor of the residual stresses resulting from the thermo-metallurgical and mechanical transformations of the materials after welding. Various numerical simulations have thus permitted the necessary data base to be established for the experimental validation of the local approach. The test programme was applied, in a first stage, to symmetrical and asymmetrical Tee joints produced by single-pass or multipass welding, and subjected to transverse loads. Lastly, we propose to apply this new method to "three-dimensional" assemblies such as tubular beams subjected to transverse bending.