Analytical equations of two-step adsorption kinetics on surface have been derived. Moreover, computer simulations have been carried out to interpret various experimental adsorption kinetics previously reported. In the first case, molecules are further adsorbed from a solution onto a layer consisting of previously adsorbed molecules. This model was applied to the adsorption kinetics of hexadecyltrimethylammonium chloride (C(16)TAC) on a self-assembled monolayer (SAM) of 3-mercaptopropionic acid (T. Imae, H. Torii, J. Phys. Chem. B 104 (2000) 9218). The second case is that some of the initially adsorbed molecules are released from the adlayer with further time course. The adsorption of C(16)TAC on 1-dodecanethiol SAM (T. Imae, T. Takeshita, K. Yahagi, Stud. Surf. Sci. Catal. 132 (2001) 477) agrees with this mechanism. The strict mathematical developments presented in this work are demanded to specify the physical meaning of observed non-Langmuir adsorption kinetics, consisting of the two exponential terms. (C) 2003 Elsevier Inc. All rights reserved.