Impurity dimers [Cu3+–Cu2+] (С2v) with an antiferromagnetic bond between copper ions have been synthesized in BaF2 crystals. The study of the molecular structure of the synthesized dimers was carried out by the electron paramagnetic resonance at frequencies of 9.3 and 34.2 GHz in the temperature range from 5 to 150 K. It was shown that the 63Cu3+ and 63Cu2+ ions replaced the neighboring cations of the Ва2+ lattice, forming a dimer with a parallel bond axis of one of the 〈110〉 crystallographic axes. It has been found that the coupling between copper ions has an antiferromagnetic exchange interaction and that its repeated inverse state is a doublet, S = 1/2. There were determined parameters of Zeeman interaction, part of the parameters of the hyperfine and quadrupole interaction of 63Cu3+ and 63Cu2+ ions, as well as part of the parameters of the ligand hyperfine interaction with two equivalent F– ions.