A method is suggested to determine the most probable values of the angles phi, psi of the protein backbone by the data on the availability and absence of d connectivities in the two-dimensional nuclear Overhauser enhancement spectra. In view of this, the dependences of the proton-proton distances in dipeptide units of L-amino acid residues on the dihedral angles phi, psi, chi1 are considered and the conformational states of amino acid residues of the proteins with the known spatial structure are analysed statistically. The potentialities of the method are assessed with the aid of model spectral nuclear magnetic resonance (NMR) parameters obtained from the X-ray data for the bovine pancreatic trypsin inhibitor and avian pancreatic polypeptide. It is shown that the developed procedure of structural interpretation of the NMR data allows one to correctly reproduce the local conformation of the protein backbone. The obtained backbone conformation may serve as a starting point to build and refine molecular three-dimensional structure.