Friedmann-Robertson-Walker universes with a presently large fraction of the
energy density stored in an X-component with w(X) < -1/3, are considered.
We find all the critical points of the system for constant equations of sta
te in that range. We consider further several background quantities that ca
n distinguish the models with different mx values. Using a simple toy model
with a varying equation of state, we show that even a large variation of w
(X) at small redshifts is very difficult to observe with d(L)(z) measuremen
ts up to z <similar to> 1 Therefore, it will require accurate measurements
in tile range 1 < z < 2 and independent accurate knowledge of Omega (m,0) (
and/or Omega (X),0) in order to resolve a variable w(X) from a constant w(X
).