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We report on picosecond pulsed response and 3-dB cutoff frequency of 1.3-mum GaNAsSb unitraveling-carrier photodetectors (PDs) grown by molecular beam epitaxy using a radio-frequency plasma-assisted nitrogen source. The 0.1-mum -thick GaNAsSb photoabsorption layer contains 3.5% of N and 9% of Sb, resulting in a bandgap of 0.88 eV. The dark current densities at 0 and -9 V are 6 and 34 mA/cm2, respectively. The GaNAsSb UTC PDs exhibit a temporal response width of 46 ps and a record 3-dB cutoff frequency of 14 GHz at -9 V.