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We report our studies on the response of ultrathin superconducting NbN hot-electron photodetectors. We have measured the photoresponse of few-nm-thick, micron-size structures, which consisted of single and multiple microbridges, to radiation from the continuous-wave semiconductor laser and the femtosecond Ti:sapphire laser with the wavelength of 790 nm and 400 nm, respectively. The maximum responsivity was observed near the film's superconducting transition with the device optimally current-biased in the resistive state. The responsivity of the detector, normalized to its illuminated area and the coupling factor, was 220 A/W(3/spl times/10/sup 4/ V/W), which corresponded to a quantum efficiency of 340. The responsivity was wavelength independent from the far infrared to the ultraviolet range, and was at least two orders of magnitude higher than comparable semiconductor optical detectors. The time constant of the photoresponse signal was 45 ps, when was measured at 2.15 K in the resistive (switched) state using a cryogenic electro-optical sampling technique with subpicosecond resolution. The obtained results agree very well with our calculations performed using a two-temperature model of the electron heating in thin superconducting films.