  We consider classical hard-core particles moving on two parallel chains in
the same direction. An interaction between the channels is included via the
hopping rates. For a ring, the stationary state has a product form. For the
case of coupling to two reservoirs, it is investigated analytically and
numerically. In addition to the known one-channel phases, two new regions are
found, in particular the one, where the total density is fixed, but the filling
of the individual chains changes back and forth, with a preference for strongly
different densities. The corresponding probability distribution is determined
and shown to have an universal form. The phase diagram and general aspects of
the problem are discussed.
