  We study classical particles on the sites of an open chain which diffuse,
coagulate and decoagulate preferentially in one direction. The master equation
is expressed in terms of a spin one-half Hamiltonian $H$ and the model is shown
to be completely solvable if all processes have the same asymmetry. The
relaxational spectrum is obtained directly from $H$ and via the equations of
motion for strings of empty sites. The structure and the solvability of these
equations are investigated in the general case. Two phases are shown to exist
for small and large asymmetry, respectively, which differ in their stationary
properties.
