  We study the contact process on layered networks in which each layer is
unidirectionally coupled to the next layer. Each layer has elements sitting on
i) Erd{\"o}s-R{\'e}yni network, ii) a $d$-dimensional lattice. The layer at the
top which is not connected to any layer. The top layer undergoes absorbing
transition in the directed percolation class for the corresponding topology.
The critical point for absorbing transition is the same for all layers. For
Erdos-Reyni network order parameter $\rho(t)$ decays as $t^{-\delta_l}$ at the
critical point for $l'$th layer with $\delta_l \sim 2^{1-l}$. This can be
explained with a hierarchy of differential equations in the mean-field
approximation. The dynamic exponent $z$ is $0.5$ for all layers and the value
of $\nu_{\parallel}$ tends to 2 for larger $l$. For a d-dimensional lattice, we
observe stretched exponential decay of order parameter for all but top layer at
the critical point.
