The adsorption of three tripeptides in an ion-exchange membrane adsorber was analyzed in single and binary solutions, with the aim of evaluating the capability of the membrane adsorber to separate triglycine (GGG) from two other tripeptides: glycine-histidine-glycine (GHG) and glycine-tyrosine-glycine (GTG). The equilibrium adsorption of single peptide solutions followed the Langmuir isotherm and GTG showed the highest adsorption affinity. The dynamic adsorption was fitted with a generalized model, which was defined using dimensionless parameters and based on the continuity equation. In general, the calculated and experimental breakthrough curves were correlated with high agreement. It was found that the axial dispersion coefficient was independent of the peptide molecule and that it increased with flow rate. The competitive adsorption between peptides in binary solutions was analyzed using the extended and modified Langmuir equations. The adsorption equilibrium data were satisfactorily fitted with the modified Langmuir isotherm for GGG/GHG solutions, while the extended Langmuir isotherm was a better fit to the data for GGG/GTG solutions. The experimental breakthrough curves of the two peptide binary mixtures were simulated using the parameters calculated from the competitive isotherms and the parameters obtained from the breakthrough curves of the single peptide solutions. The separation of GGG from the GGG/GHG mixtures was possible. The GGG recovery was higher than 35% and the GGG molar fraction in the outlet stream was higher than 0.994.