  We present an autonomous phase-plane describing the evolution of
Friedmann-Robertson-Walker models containing a perfect fluid (with barotropic
index gamma) in Brans-Dicke gravity (with Brans-Dicke parameter omega). We find
self-similar fixed points corresponding to Nariai's power-law solutions for
spatially flat models and curvature-scaling solutions for curved models. At
infinite values of the phase-plane variables we recover O'Hanlon and Tupper's
vacuum solutions for spatially flat models and the Milne universe for negative
spatial curvature. We find conditions for the existence and stability of these
critical points and describe the qualitative evolution in all regions of the
(omega,gamma) parameter space for 0<gamma<2 and omega>-3/2. We show that the
condition for inflation in Brans-Dicke gravity is always stronger than the
general relativistic condition, gamma<2/3.
