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Research determined the molecular arrangements of two copper(II) dipeptide complexes with the use of the combined electron paramagnetic resonance spectroscopy, second derivative displays and computer simulation techniques. The ionic and covalent nature of the metal-ligand bonds of the two copper dipeptides, Cu-GlyHis and CuHisGly complexes, are also examined. Results show two different dipeptide arrangements in the first coordination sphere. The combined approaches was also found to be effective in identifying a set of spin Hamiltonian input parameters for the copper dipeptides.