We report strong evidence for coherent modes of moving Josephson vortices in mesas patterned on the surface ofBi2Sr2CaCu2Oxsingle crystals. The vortex flow current–voltage curves are characterized by a sharp up-turn and the appearance of multiple branches as the current is ramped up and down at a fixed magnetic field and temperature. These results are consistent with weakly damped motion of Josephson vortices in which different coherent modes can occur in a close stack of Josephson coupled multilayers. ©1997 American Institute of Physics.