ZnO nanowire (NW) visible-blind UV photodetectors with internal photoconductive gain as high as G approximately 108 have been fabricated and characterized. The photoconduction mechanism in these devices has been elucidated by means of time-resolved measurements spanning a wide temporal domain, from 10-9 to 102 s, revealing the coexistence of fast (tau approximately 20 ns) and slow (tau approximately 10 s) components of the carrier relaxation dynamics. The extremely high photoconductive gain is attributed to the presence of oxygen-related hole-trap states at the NW surface, which prevents charge-carrier recombination and prolongs the photocarrier lifetime, as evidenced by the sensitivity of the photocurrrent to ambient conditions. Surprisingly, this mechanism appears to be effective even at the shortest time scale investigated of t < 1 ns. Despite the slow relaxation time, the extremely high internal gain of ZnO NW photodetectors results in gain-bandwidth products (GB) higher than approximately 10 GHz. The high gain and low power consumption of NW photodetectors promise a new generation of phototransistors for applications such as sensing, imaging, and intrachip optical interconnects.