8 new models, named respectively LK 1, LK 2, LK 3, LEq 1, LEq 2, LEq 3, LEq 4 and LEq 5 are suggested to describe the kinetics and the equilibrium of a homogeneous adsorption. The models, more general than the existing ones, are very useful to describe the different kinetics and isotherms experimental behaviour of many adsorbents. In these new methods, the adsorption is decomposed in 1 or 2 steps, each step following an n order kinetics. The models have scientific, logical and chemical understanding meaning. Some (LK 1, LK 3, LEq 2, LEq 4) can predict the maximum adsorption capacity Q(max). LEq 1 and LEq 2 models permit to make the link between the kinetics and the equilibrium results and determine the order of reaction for both the adsorbent and the adsorbate, then, increasing the knowledge of the sorption parameters. The kinetics and the equilibrium of the adsorption of lead by a commercial activated carbon are studied and these new models are used to fit the experimental data. The kinetics and the equilibrium parameters are determined. The fitting of the kinetics results are compared to those obtained with other existing models, idem for the equilibrium results. Regression results show that the new equilibrium models better fit the experimental data than the existing ones for this sorption process. (C) 2016 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.