We present a surface force apparatus (SFA) study of the effects of time and loading-unloading rates on the adhesion of solid polymeric surfaces of poly(butylmethacrylate). We used the equilibrium JKR theory of adhesion or contact mechanics as a framework for analyzing the "adhesion dynamics" of two surfaces during nonequilibrium (viscoelastic, plastic) adhesion and separation. PBMA films of thickness similar to 2 mu m were prepared on curved mica surfaces by casting from a solution of methyl ethyl ketone. Pull-off forces from adhesive contact were measured at different temperatures around the glass-rubber transition temperature (T-g approximate to 25 degrees C) at different loads and contact times, and hysteretic loading-unloading cycles were measured at different rates. On entering the rubber regime, the effective surface energies deduced from the pull-off forces increase dramatically, by up to 3 orders of magnitude above the "equilibrium" value, with increasing contact time and load. Strong entanglements across the interface, probably through reptation, increase the effective area of contact with time, giving rise to the high pull-off forces observed. Bulk viscoelastic deformations of the surface profiles accompany the time-dependent adhesion processes. The existence of at least two different relaxation (energy dissipating) processes, one at the molecular level and the other at the microscopic to macroscopic level, can be inferred from these experiments. The implications of the results for understanding the adhesion, fracture strength, and crack-propagation of elastic Versus viscoelastic materials are discussed.