One of the current trends in polymer chemistry is to improve the properties of common polymers in order to replace more expensive specific materials. For instance, the presence of a small number (about one or less per polymer chain) of long chain branching (LCB) can increase processability of polymers without reduction of their mechanical resistance. It is thus very important to characterize precisely the molecular structure of branched polymers: their molar mass distribution (MMD), number and length of the branches , evolution of the branching content with molar mass, A complete method of characterization of the molecular structure of slightly branched polymers thanks to Size Exclusion Chromatography (SEC) coupled with viscometry is developed in this work. In order to ensure its validity, it is based on the characterization of model polymers, for which the branching number is known from the synthesis. After the optimization of the treatment of the chromatograms thanks to linear polymers, anionic three arms polystyrene stars, blends of them with broad MMD linear polystyrene as well as randomly branched polycarbonates have been analysed. It is shown that the rheological definition of a long chain branching can be used in SEC viscometry and that the lower molar mass limit for LCB characterization by this technique about 30 000 g/mol. Its detection limit is 1 LCB /2-3 polymer chains. However, if branching is located near one end of the MMD, the analyses of fractions where the branched chains are concentrated can be helpful. Qualitatively, the presence of LCB can be detected by the observation of the evolution of intrinsic viscosity with retention time. For a semi-quantitative analysis, a branching parameter obtained at constant retention time instead of constant molar mass is shown to give reproducible results. For quantitative analysis, g is calculated at the top of the chromatographic peak for low polydispersity polymers and for each fraction of broad MMD polymers. Using this method, a classification linking g and the LCB number was finally set up. ...