  We consider classical hard-core particles hopping stochastically on two
parallel chains in the same or opposite directions with an inter- and
intra-chain interaction. We discuss general questions concerning elementary
excitations in these systems, shocks and rarefaction waves. From microscopical
considerations we derive the collective velocities and shock stability
conditions. The findings are confirmed by comparison to Monte Carlo data of a
multi-parameter class of simple two-lane driven diffusion models, which have
the stationary state of a product form on a ring. Going to the hydrodynamic
limit, we point out the analogy of our results to the ones known in the theory
of differential equations of conservation laws. We discuss the singularity
problem and find a dissipative term that selects the physical solution.
