Organic monolayers were formed on mica substrates whose detachment was rate-independent in the absence of these monolayers. The pull-off force under dry conditions was measured as a function of contact time (0.01-500 s) and separation rate (0.003-100 mu m/s; corresponding lateral crack velocity approximately 0.04-1200 mu m/s) using a piezoelectric bimorph attachment to a surface forces apparatus. No time or rate dependence was observed for close-packed crystalline monolayers of condensed n-octadecyltriethoxysilane (OTE) or the adsorbed glassy diblock copolymer poly-2-vinylpyridine (PVP)-polystyrene, Rate dependence beyond a critical separation rate was observed in monolayers whose chains were more mobile although anchored at one end to the solid surface. For loose-packed monolayers of cetyltrimethylammonium bromide (CTAB), the adhesion in excess of the constant observed at low rate increased as a power law with the square root of the separation rate. For adsorbed PVP-polybutadiene, the excess adhesion increased nearly linearly with the logarithmic separation rate. For both CTAB and PVP-polybutadiene, the critical separation rate lessened with increasing contact time before detachment. The time effects are ascribed to interdigitation between the contacting layers as a result of interdiffusion over nanoscale distances, facilitated by the low glass transition of the polybutadiene and the loose packing of the CTAB monolayers. The rate effects are ascribed to viscoelasticity during chain pull-out. The rate dependence was weaker than the simple proportionality to velocity that has been expected theoretically for chain pull-out. The oft-proposed separation of rate-dependent adhesion into the product of bulk viscoelastic response and a constant surface energy is inconsistent with these findings.