The dynamics of magnetic fluxons in a system of two vertically stacked long Josephson junctions is investigated numerically. The model is based on the approach by S. Sakai, P. Bodin, and N. F. Pedersen [J. Appl. Phys. 73, 2411 (1993)] and is described by two strongly coupled sine-Gordon equations. In agreement with recent experimental data, we confirm numerically the effect of splitting of the fluxon travelling mode into two separated modes with different characteristic velocities. The simulated current-voltage characteristics indicate stable phase-locked flux-flow resonances of two junctions. These results support a possibility of application of the stacked long Josephson junctions as a system of coherent oscillators for millimeter and sub-millimeter wave bands. ©1995 American Institute of Physics.