We use a simple two-order parameter model to describe the interaction between the brushes of polymers terminally attached to flat surfaces immersed in a supercritical solvent. Our approach makes it possible to take into account the high compressibility of the supercritical solvent, which proves to give a significant contribution to the disjoining force acting between polymer brushes. Our theory explains why the interaction between brushes can change from repulsive to attractive with decreasing solvent density. This theoretical finding is verified by making a comparison with recent computer simulations. A reasonably good agreement between the results of the present theory and the simulations is found. (C) 2004 American Institute of Physics.