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The focus of this paper is the evaluation of the new fast 51 mm-diameter, 8-stage Hamamatsu R9779 photomultipliers (PMTs) with an acceleration-ring at the front-end and the Photonis XP20D0 PMTs with a screening grid in front of the anode. The following performance characteristics are presented: Timing resolution, anode-scan-uniformity and transit-time spread. The unfolded timing resolution for two R9779 was 192 ps and 210 ps using plastic scintillators. The individual timing resolutions for two XP20D0 using plastic scintillators are 181 ps and 154 ps, respectively. The variation in time resolution across the windows of the two R9779 ranged between 117 ps and 171 ps, and 79 ps and 73 ps for the two XP20D0 PMTs.