  Recently it has been shown that the transition of the 1+1-dimensional
annihilation-fission process 2X->3X, 2X->0 exhibits an unusual type of
nonequilibrium critical behavior. The phenomenological properties of critical
clusters are characterized by two different dynamic modes for spreading and
diffusion. In order to describe the interplay of these modes, we introduce an
effective model which involves two species of particles A and B. The
A-particles perform an ordinary directed percolation process while the B
particles diffuse and annihilate. Both subsystems are cyclically coupled by
particle transmutation A <-> B. The resulting critical behavior is in many
respects similar to the one observed in the annihilation-fission process.
