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We study PdPt bimetallic clusters in both free and supported phases. These clusters have been produced with a laser vaporization source. Free clusters directly produced by the source are studied by time of flight mass spectrometry and photofragmentation technique. We observed a sequential evaporation of Pd atoms in the mixed clusters consistent with a palladium segregation process. This tendency has been also observed on supported particles from which the structure and the composition are determined by high resolution transmission electron microscopy and energy dispersive x-ray analysis. A main result is that each particle has the composition of the massic rod vaporized in the source. The supported particles are well crystallized and exhibit truncated octahedron shapes. Experimental observations are well explained using a modified tight binding model. Indeed, within this model, we found that the equilibrium shape is strongly related to the variation of the cohesive energy with atomic coordination number. Also, some preliminary results on the specific reactivity of these bimetallic clusters are presented.