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We have numerically and experimentally studied on the Josephson-vortex flow in stacks of intrinsic Josephson junctions in Bi2Sr2CaCu2Oy single crystals. Numerical simulations of static and dynamic behavior of Josephson vortices in such a stack were carried out by using perturbed coupled sine-Gordon equations. The current-voltage characteristics of the stacks in the single-crystal mesas were measured without or with magnetic field B up to 4.5 T parallel to the junction layers at 4.2 K. It has been observed that the vortex flow tends to occur preferably in the highest velocity mode (in-phase mode) only in several junctions in the stack in low B below ∼1 T, in intermediate velocity modes in more junctions in it in intermediately higher B and preferably in the lowest velocity mode (out-of-phase mode) in almost all junctions in it in much higher B above ∼2.5 T, accompanied by a decrease in flow velocity from ∼2.5×106 to (2-5)×105 m/s with increasing Bfs. This behavior of vortices can be interpreted to arise from an increase in interaction among vortices in the stack with the increase in B, according to the simulated results.