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Discrete conductance increments in the current-voltage characteristics of superconductor-insulator-superconductor tunnel junctions (of area ⪕25 μ m 2 ) associated with single flux quanta (“vortices”) trapped in the thin film electrodes have been observed. These tunneling results were obtained for both Sn and Pb and provide, for the first time, a direct measure of the density of quasiparticle states corresponding to a single vortex. Simultaneous measurements of the Josephson critical current suppresion indicate that the vortex cores are on the average not aligned across the barrier on the scale of the coherence lenght. The measured vortex density of states is in disagreement with predictions of the normal cores model and previously published data.