  We provide a detailed description for power--law scaling
Friedmann-Robertson-Walker cosmological scenarios dominated by two interacting
perfect fluid components during the expansion. As a consequence of the mutual
interaction between the two fluids, neither component is conserved separately
and the energy densities are proportional to $1/t^{2}$. It is shown that in
flat FRW cosmological models there can exist interacting superpositions of two
perfect fluids (each of them having a positive energy density) which accelerate
the expansion of the universe. In this family there also exist flat power law
cosmological scenarios where one of the fluids may have a ``cosmological
constant" or "vacuum energy" equation of state ($p =-\rho$) interacting with
the other component; this scenario exactly mimics the behavior of the standard
flat Friedmann solution for a single fluid with a barotropic equation of state.
These possibilities of combining interacting perfect fluids do not exist for
the non-interacting mixtures of two perfect cosmic fluids, where the general
solution for the scale factor is not described by power--law expressions and
has a more complicated behavior. In this study is considered also the
associated single fluid model interpretation for the interaction between two
fluids.
