Electron paramagnetic resonance (EPR) of single-crystal [Cu(PU)5(ClO4)2]2, built of dimeric fragments with P symmetry, Z = 1, and ClO4 anions, was studied over a range of temperatures at both X and Q band frequencies. EPR spectra show the presence of exchange interaction J(S1 · S2) (J < 0) between two identical Cu2+ ions (S 1 = S 2 = 1/2) in the dimeric fragment. The single-crystal spectra recorded in three different planes were analysed by diagonalization of the full Hamiltonian matrix. The values of g and D were found to have coincident y axes, with the x and z axes rotated by 45°. The tensor of the dipole-dipole interaction was calculated. Two variants for the anisotropic exchange interaction tensor were determined. The data obtained from the analysis of the single-crystal spectra were used to simulate the polycrystalline spectrum. The peculiarities of the polycrystalline spectra for centres S = 1 with nonparallel g and D tensors and the possibilities of their unambiguous interpretation are discussed. The double-quantum transition in single-crystal and polycrystalline spectra was detected.