Kinetics and equilibrium of the ion exchange of Cd2+ at Na-montmorillonite are investigated and analyzed for the first time by kinetic and affinity spectra. To obtain these distribution functions an inverse integral transformation is performed numerically by the program CONTIN with the integral adsorption equation. It employs the constrained regularization technique with a smoothing regularizer favoring parsimony of the solution and an automatic adjustment of the regularization strength by the statistical F test. A Langmuir equation as local isotherm is additionally built in the code for the first time so that CONTIN is now a very convenient and handy tool for the calculation of model independent kinetic and affinity spectra. Bimodal kinetic spectra are observed where the main process (80%) is the binding of Cd2+ at the outer surface. The mean rate coefficient k(mean) is 11 s(-1) at 25 degrees C and the HWHH of the distribution function of about 0.1 log k units proves the considerable degree of heterogeneity. An inner sphere complex is formed that is controlled by the ion exchange reaction itself, not by diffusion, as proven by temperature dependent measurements. The more heterogeneous slow process is caused by aggregation of the platelets and intercalation of Cd2+ into the interlayer space. A broad monomodal affinity spectrum is found with a mean value of log K-ex,K-mean = 0.5 and an asymmetry to the low affinity side.