We investigate the behavior of solutes undergoing nonequilibrium adsorption processes that lead to a Freundlich isotherm in equilibrium. In contrast to a frequently used model we do not assume that the adsorption rate is proportional to the difference between adsorbed and equilibrium concentrations, but inspect two nonlinear laws governing the path to equilibrium. With some asymptotic considerations and numerical simulations we find that depending on the model parameters, the concentration in solution and the mass adsorbed by the matrix do not necessarily reach quasiequilibrium.