Considering the most general one-species reactiondiffusion processes on a Cayley tree, it has been shown that there exist two integrable models. In the first model, the reactions are the various creation processes, i.e. ! , ! and ! , and in the second model, only the diffusion process ! exists. For the first model, the probabilities Pl.mI t/, of finding m particles on the lth shell of the Cayley tree, have been found exactly, and for the second model, the functions Pl.1I t/ have been calculated. It has been shown that these are the only integrable models if one restricts consideration to the L C 1-shell probabilities P.m0;m1; : : : ;mLI t/.
