A great number of copper(II) complexes that have as ligands biological compounds have been used as models for the understanding of several reactions that occur in vivo. Several neurodegenerative disorders are characterized by the abnormal presence of proteins in the central nervous system that have a high affinity for the copper(II) ion. This coordination of metal to proteins favor the deposition process and associated the production in excess of reactive oxygen species (ROS) occurs. The methionine is an antioxidant present in the biological medium that could bind to copper and prevent the oxidative damages. In the present work we studied in aqueous solution the binary complexes Cu(II):L1 and Cu(II):L2 and the ternary complex Cu(II):L1:L2 (L1 = GlyGly and L2 = Met) at 25C and μ = 0.1 mol L-1. The binding constants of the complexes were determined using the BEST7 program. The coordination modes of the ligands in the Cu(II) complexes were investigated by DFT calculation using the TURBOMOLE 6.1 program. The PBE functional was used employing the resolution of identity approximation (RI-J) and with the def2-SVP basis set. The solvent effects were included through the COSMO solvation model. The DFT results showed bidentate behavior of the glycylglycine in the Cu(H-1GlyGly) species without the participation of the oxygen from the carboxylic group in the metal coordination sphere. The cluster-continuum model was used to obtain for the more stable complexes the free energies in gas phase and in the aqueous solution through DFT methods: B3LYP/def2/TZVP and PBE0/def2-TZVP. The second solvation shell (36 water molecules) was included in the more stable complexes to verify the interference of solvent explicit molecules in the calculation. The results showed monodentate behavior of the glycylglycine ligand in the complex [Cu(GlyGly)(H2O)36]+, without the participation of the peptidic oxygen in coordination sphere of metallic centre. It was observed that the clusters assume different geometries: octahedral ([Cu(Met)(H2O)36]+), square pyramid ([Cu(GlyGly)(H2O)36]+, [Cu(H-1GlyGly)(H2O)36], [Cu(Met)(OH)(H2O)36], [Cu(Met)(OH)2(H2O)36]-, [Cu(HGlyGly)(Met)(H2O)36], [Cu(GlyGly)(Met)(H2O)36]- and [Cu(GlyGly)(Met)(OH)(H2O)35]2-) and distorted square ([Cu(GlyGly)(OH)(H2O)35]-). All the clusters presented an electronic configuration of ground state t6 2g d22 d1 x2-y2 that agree with the Jahn-Teller distortion. In the neurodegenerative diseases the physiologic pH is slightly acidified. In the ternary species [Cu(GlyGly)(Met)(H2O)36]-, that is formed in pH 7, the sulfur is not part of the coordination sphere of copper, indicating that it could exert an antioxidant action in biological systems under oxidative stress conditions.