  We study the dynamics near finite-time singularities of flat isotropic
universes filled with two interacting but otherwise arbitrary perfect fluids.
The overall dynamical picture reveals a variety of asymptotic solutions valid
locally around the spacetime singularity. We find the attractor of all
solutions with standard decay, and for `phantom' matter asymptotically at early
times. We give a number of special asymptotic solutions describing universes
collapsing to zero size and others ending at a big rip singularity. We also
find a very complicated singularity corresponding with a logarithmic branch
point that resembles of cyclic universe, and give an asymptotic local series
representation of the general solution in the neighborhood of infinity.
