Permanganate (MnO–4 ) ions were adsorbed on carbonate intercalated Co-Al-layered double hydroxide (Co-Al-LDH) and MoS2 and after a while the adsorbed MnO–4 ions were reduced to MnO2. Reduction of adsorbed MnO–4 ion was catalyzed on the surface of carbonate intercalated Co-Al-LDH but MnO–4 ions reacted with MoS2 surface. Adsorption kinetic tests were carried out at different temperatures, ionic strengths, pH, initial adsorbate concentrations and shaking rates. The adsorption kinetics was studied by the kinetics of adsorption study in the regions with constant adsorption acceleration (KASRA) model and KASRA, ideal-second-order (ISO), intraparticle diffusion, Elovich and (non-ideal process of adsorption kinetics (NIPPON) equations. In this work, a new equation called NIPPON equation was introduced. In this equation, it was assumed that during a non-ideal process, adsorbate species molecules were adsorbed simultaneously on the same type adsorption sites with different activities. Indeed, the average values of adsorption kinetic parameters were calculated by the NIPPON equation. Also, the character of boundaries of regions obtained from the KASRA model can be determined by this equation.