  We study curved isotropic cosmologies filled with two interacting fluids near
their time singularities. We find that a number of these universes asymptote to
flat limits in the sense that their asymptotic properties become
indistinguishable from those of flat Friedmann-Robertson-Walker models on
approach to the singularity along any asymptotic direction. In particular,
there are no essential singularities in these models. We discuss connections of
this result with possible extensions of the cosmic no hair theorem to the case
of two interacting fluids, and also provide links to a quantum cosmological
treatment of real and complex Euclidean such solutions.
