This thesis deals with the structure and reactivity of alumina supported palladium clusters used as model catalysts. The main purpose of this work is to depict the support effect on the nucleation and reactivity of the metal phase taking explicitly into account the surface hydration. We studied clusters containing from 1 to 13 atoms. Firstly, the structure of supported clusters was assessed. Two interaction modes were found. The results on this thesis put forward that small aggregates (<3 atoms) present a strong interaction with the support, which induces a strong deformation of the surface oxide. As for bigger aggregates, the results show that the interaction with the support is weaker and that their structure is governed by Pd-Pd interactions. Moreover, the reactivity of size 4 aggregates has been studied by means of model calculations on the adsorption of CO and ethene. The results from this study allow the determination of size and support effects induced by the alumina support. Some important qualitative conclusions are drawn from the results in this work.