  Unidirectionally coupled systems which exhibit phase transitions into an
absorbing state are investigated at the multicritical point. We find that for
initial conditions with isolated particles, each hierarchy level exhibits an
inhomogeneous active region, coupled and uncoupled respectively. The particle
number of each level increases algebraically in time as $N(t) \sim t^{\eta}$
with different exponents $\eta$ in each domain. This inhomogeneity is a quite
general feature of unidirectionally coupled systems and leads to two
hyperscaling relations between dynamic and static critical exponents. Using the
contact process and the branching-annihilating random walk with two offsprings,
which belong to the DP and PC classes respectively, we numerically confirm the
scaling relations.
