The results of an investigation of the characteristics of photomultipliers for the Deep Underwater Muon and Neutrino Detection (DUMAND) System are discussed. The pulse-height resolution, the afterpulsing phenomena and the gain sensitivity to the ambient magnetic field have been determined for large photocathode area photomultipliers. Furthermore, the transient time difference, the single photoelectron time spread, and the collection and photocathode quantum efficiency uniformity as a function of the position of the photocathode sensing area have been reviewed. Finally, an attempt has been made to estimate the photomultiplier reliability and its lifetime.