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We report room-temperature optical reflectivity and transmission measurements on a variety ofYBa2Cu307 and Bi2Sr2Can -1CUn02n +4 thin films in the 500-25000 cm-1 frequency range. Reflectivitydata when not biased by the substrate are used to compute the optical conductivity. A comparison ofour results with published reflectivity data on single-domain YBa2Cu307 crystals suggests an overwhelmingcontribution of the CU02 planes {with respect to the chains} to the optical conductivity. The datacan be analyzed in terms of a Drude low-frequency contribution and a so-called midinfrared band. However,the anomalous infrared response appears to be uniquely described by a generalized Drude response:for all the samples investigated, the relaxation rate (which increases linearly with frequency) and theeffective mass are found to be the same as a function of frequency.