An extension of the multifluid approach to the description of heavy-io
n collisions is proposed. A three-fluid model involving mean sigma and
omega fields is formulated for heavy-ion collisions at incident energ
ies around 1 GeV per nucleon. It is a natural extension of a similar t
wo-fluid model developed in our recent papers and is intended to obtai
n a closer approximation to the complete relativistic mean-field kinet
ic theory. The collisional coupling between the fluids is formulated i
n terms of hadron-hadron cross sections (which take into account Pauli
blocking). The model contains no fitting parameters. The relativistic
mean-field three-fluid model mean field three-fluid model (RMF-3FM) i
s tested for the case of thermalization in counter-streaming nuclear f
luids. Comparison with the results obtained in relativistic Landau-Vla
sov kinetics and in a similar two-fluid model (RMF-2FM) shows that the
RMF-3FM reproduces the gross properties of the equilibration better t
han the RMF-2FM.