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Broadband Dielectric Spectroscopy is employed to investigate the molecular dynamics in thin films of hyperbranched polyesters (type AB1B2, with -OH and -OCOCH3 as terminal groups). Three relaxation processes are detected: alpha, beta and gamma. While the latter two are not influenced by the confinement, a pronounced effect is observed on the alpha relaxation: with decreasing film thickness the slower relaxation modes of the dynamic glass transition are gradually suppressed, resulting in an increase of the average relaxation rate and in a linear decrease of the dielectric strength. This is attributed to an immobilization in confinement of the polymeric segments located at the periphery of the hyperbranched macromolecular structures.