  We study propagation of pulses along one-way coupled map lattices, which
originate from the transition between two superstable states of the local map.
The velocity of the pulses exhibits a staircase-like behaviour as the coupling
parameter is varied. For a piece-wise linear local map, we prove that the
velocity of the wave has a Devil's staircase dependence on the coupling
parameter. A wave travelling with rational velocity is found to be stable to
parametric perturbations in a manner akin to rational mode-locking for circle
maps. We provide evidence that mode-locking is also present for a broader range
of maps and couplings.
