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PACS 74.78.Fk, 85.25.Oj We present our progress on the research and development of NbN superconducting single-photon detectors (SSPD's) for ultrafast counting of near-infrared photons for secure quantum communications. Our SSPD's operate in the quantum detection mode based on the photon-induced hotspot formation and subsequent development of a transient resistive barrier across an ultrathin and submicron-width superconducting stripe. The devices are fabricated from 4-nm-thick NbN films and kept in the 4.2-to 2-K temperature range. The detector experimental quantum efficiency in the photon-counting mode reaches above 40% for the visible light and up to 30% in the 1.3-to 1.55-µm wavelength range with dark counts below 0.01 per second. The experimental real-time counting rate is above 2 GHz and is limited by our readout electronics. The SSPD's timing jitter is below 18 ps, and the best-measured value of the noise-equivalent power (NEP) is 5 × 10 -21 W/Hz 1/2 at 1.3 µm. In terms of quantum efficiency, timing jitter, and maximum counting rate, our NbN SSPD's significantly outperform semiconductor avalanche photodiodes and photomultipliers in the 1.3-to 1.55-µm range.