The near fine structure of absorption K-spectra of oxygen atoms in Cu2O and CuO copper oxides is studied by using an RSM-500 X-ray spectrometer-monochromator and bremsstrahlung of an X-ray tube with a tungsten cathode by the method of the quantum yield of the extrinsic X-ray photoeffect. Resonant features in the structure of spectra obtained, as well as Cu L3- and Cu K-absorption spectra and isochromates of X-ray bremsstrahlung spectra of oxides known from the literature, are considered within the framework of the quasimolecular approach. The analysis performed resulted in the identification of all the form resonances on the basis of transitions of core electrons to free molecular orbitals (MO) of O-Cu-O and CuO4 quasi-molecules (structural units) for Cu2O and CuO, respectively, and the determination of the symmetry and the composition of these MO and their energy positions with respect to the immobile MO constructed mainly of 2pπ-states of an oxygen atom. The most important distinction of the systems of free MO of oxides obtained is found to be in significantly different positions of free Cu 3d-states with respect to O 2pπ-states. Experimental evidence for the participation of 3d-electrons of a copper atom in the formation of the chemical bond in Cu2O is noted. The important role of reemission from the lowest excited state in the formation of the O Kα-emission spectrum of CuO obtained by other authors by the fluorescent method is found.