Magnetic field dependence of current-voltage characteristics of 7-layer stacked Nb/Al-AlO/sub x//Nb long Josephson junctions are investigated experimentally. The magnetic coupling between the junctions is provided by their common superconducting electrodes of the thickness smaller than the London penetration depth. The current-voltage characteristics clearly display collective flux-flow behaviour of Josephson vortices (fluxons) which simultaneously move in up to 5 layers of the stack under the influence of the bias current. The flux-flow behaviour is modulated by a complicated structure of cavity-like resonances which show a broad range of characteristic frequencies. Our observations can be qualitatively explained as the interplay between the Fiske modes and the two-dimensional resonances in these stacks. For the intermediate magnetic field range, we find pronounced resonant modes with large voltage spacing which indicates mutually coherent operating junctions.