We study experimentally and theoretically the influence of phase-whirling (resistive) state in one junction of a twofold Josephson stack on the fluxon motion in the other junction. In experiment, we measure the fluxon velocity versus current in one junction as a function of the state (Meissner or resistive) of the neighboring junction. The analysis, made for the limit of high fluxon density, shows that the interaction with the resistive state results in an increase of the effective damping for the moving fluxon and, therefore, in reduction of its velocity. Numerical simulations confirm this result for various fluxon densities. The experimental data are in good agreement with the theoretical predictions. In addition, the fluxon step measured experimentally has a rather peculiar structure with back and forth bending regions which is understood as a manifestation of the photon absorption in the neighboring junction.