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Polycrystalline ZnSe films of thicknesses 54-785 nm deposited on glass substrates by thermal evaporation were investigated. X-ray diffraction analysis was carried out on as-deposited and annealed films to determine their structure. The ZnSe films were polycrystalline of cubic structure with preferred [1 1 1] orientation. Transmission and reflection at normal incidence were performed on ZnSe films in the wavelength range 350-2500 nm to determine the optical constants and optical energy gap. The optical gaps of ZnSe films show remarkable dependence on the film thickness. Analysis of the absorption data revealed the existence of two transition processes (with energy gaps at 2.7 and 2.22 eV for the bulk ZnSe).