We present a detailed analysis of the interaction between two fluxon c
hains in parallel magnetically coupled long Josephson junctions, one o
f which is biased (''generator'') while another is unbiased (''detecto
r''). The main effect is that the driven fluxon chain in the generator
may drag the chain in the detector. We note that five different regim
es of the interaction are possible: both chains may be pinned by the e
xternal magnetic field; both may move in a locked state, inducing the
same de voltage in both junctions; in an unlocked state they may move
at different velocities; the chain in the detector may remain pinned w
hile the one in the generator is moving: and, finally, in a limited ra
nge of parameters the mean detector voltage may be negative, which imp
lies that the detector chain is moving in the direction opposite to th
at of the chain in the generator. We consider a simplified model based
on the assumptions that the fluxon chains are dense and rigid, and th
at their motion is nonrelativistic. In this model, each chain is repre
sented by a single degree of freedom (its coordinate). Numerical and a
nalytical consideration of the simplified model demonstrates that it i
s able to reproduce correctly all the dynamical regimes except for the
negative-voltage one. To explain the existence of the latter regime,
we introduce another model, suggested by the simulations, which is bas
ed on the presence of two fluxons and one antifluxon in the generator,
and a single fluxon in the detector. The negative voltage is produced
by motion of the antifluxon in a bound state with the detector's flux
on. The existence region of this state is limited by its collisions wi
th free fluxons in the generator.