The characteristics of the time-of-flight system of scintillation counters with the Phiepsilon3Y-527 and R5505 fine-mesh-dynode photomultipliers for high-magnetic-field environment were measured. Scintillation counters with thin plastic scintillators 1, 3, and 5 mm thick were designed to operate in comparatively strong stray magnetic fields of up to several kilogauss. The measurements were carried out in beams of the U-10 proton synchrotron (Institute of Theoretical and Experimental Physics) with proton, pi(+)-meson, and pi(-)-meson momenta of 0.63, 1.03, and 1.28 GeV/c. For counters with scintillator sizes of 1 x 20 x 154 min (BI-408) and 3 x 20 x 200 and 5 x 20 x 200 mm (Kuraray and SCSN-81), time resolutions of 45-180 ps were obtained. The time resolution of the scintillation counters, in which scintillators similar to20 mm thick and Phiepsilon3Y-527 photomultipliers. were used, was found to be 50-80 ps.