  The behavior of two interacting populations, ``hosts''and ``parasites'', is
investigated on Cayley trees and scale-free networks. In the former case
analytical and numerical arguments elucidate a phase diagram, whose most
interesting feature is the absence of a tri-critical point as a function of the
two independent spreading parameters. For scale-free graphs, the parasite
population can be described effectively by
Susceptible-Infected-Susceptible-type dynamics in a host background. This is
shown both by considering the appropriate dynamical equations and by numerical
simulations on Barab\'asi-Albert networks with the major implication that in
the termodynamic limit the critical parasite spreading parameter vanishes.
