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Summary form only given. We describe a novel technique to determine the homogeneous linewidths of surface plasmon resonances of metal nanoparticles in the presence of inhomogeneous broadening and thus measure the decay time T/sub 2/. The method is based on spectral hole burning in the inhomogeneously broadened absorption profiles of metal nanoparticles and has been applied to supported oblate Ag clusters with radii of 7.5 nm. From the experimental results and a theoretical model of hole burning the linewidth of 260 meV corresponding to a decay time of 4.8 fs was extracted. This value is shorter than expected for damping by bulk electron scattering. We conclude that additional damping mechanisms, in particular surface scattering, come into play if the electrons are confined in particles with sizes below 10 nm. Furthermore, an influence of the shape of the clusters on the decay time was observed.