Extended X-ray absorption fine structure (EXAFS) spectroscopy has been used to follow the structural evolution of the monometallic Pt/Al2O3 and the bimetallic Pt-Re/Al2O3 systems during reduction and sulfidation treatments. After sulfidation a second reduction has been performed in order to study the elimination of reversibly adsorbed sulfur. For the monometallic system, starting from the reduced state, the number of platinum-platinum bonds decreases significantly from 4.5 to 1.5 after sulfidation and a second reduction. In addition, a significant amount of sulfur is measured around platinum atoms (3 sulfur atoms per platinum atom). On the contrary, for the bimetallic platinum-rhenium system, the number of sulfur atoms in the vicinity of platinum atoms is smaller (1 sulfur atom per platinum atom) with no major change for the number of platinum-platinum bonds. Simultaneous measurements at the rhenium absorption edge show that the sulfur atoms are preferentially fixed by the rhenium atoms (2 sulfur atoms per rhenium atom). From these quantitative results, a structural model for both the monometallic and the bimetallic systems is proposed to describe the different behaviors.