The deformation and adhesion of soft elastic particles interacting with a Lennard-Jones potential is obtained by solving self-consistently the elasticity equations. Hysteresis is demonstrated between loading and unloading. Also, the pull-off force or maximum adhesion is shown to increase and eventually to saturate as the maximum applied load is increased. The origin of both of these phenomena, which have been observed experimentally, is traced to limited equilibration and dynamic hysteresis of the shape and contract angle between the advancing and receding deformed solids.