A method of calculating the singularities of two-dimensional correlation spectra of powders and determining the structural parameters with the help of a computer program is described. The opportunities of the method are illustrated on examples of experimental 2М exchange 13 C NMR spectra of dimethylsulfone, 2М exchange 2 H NMR spectrum of hexamethylbenzene, and model 2М exchange nutational NQR spectrum for spin I = 3/2.2М exchange NMR spectroscopy of a solid in the presence of anisotropic interactions is used to obtain information directly on the solid structure by means of direct measurement of stepwise reorientation (or diffusive motion) angles [1][2][3][4].Up to now nutational NMR spectroscopy has been used mainly to determine the quadrupole bond constant and the asymmetry parameter of the electric field gradient tensor of the examined nuclei. The development of 2М exchange nutational spectroscopy of a solid allows new information on the atomic and molecular composition and on the structure and internal dynamic processes to be obtained by introducing one more nuclear magnetization quantization direction (namely, the direction of the radio-frequency field B 1 ) [5].In the 2М experiment, each transverse magnetization component of the sample at the end of the first pulse from the applied pulse train acquires not only a precession phase but also a nutation phase depending on the nutation frequency (the function B 1 and angles θ and ϕ). Both precession and nutation frequencies of nuclear spins can change during the mixing period due to the molecular group reorientation. Different precession and nutation frequencies before and after mixing are correlated in the presence of molecular reorientation.On the basis of this approach, a method of determining mutual orientations of molecular interaction tensors based on the singularities of 2М exchange nutational spectra of powders is suggested.In an isotropic powder in which molecules are randomly oriented with respect to the magnetic field B 0 , the Pake singlet with two singularities is observed for spin I = 1/2 (for example, of the 13 C nucleus). In the presence of stepwise reorientations (exchange motion), the 2М spectrum of powders has characteristic crests formed by the singularities. For the axial symmetry (η = 0) and reorientation determined by one Euler's angle (α = γ = 0), these crests are shaped as two perpendicular straight lines and an ellipse; the ratio of the ellipse semiaxes determines the reorientation angle β. The shape of the dominating crests of 2М exchange spectra (of their frequency singularities) is completely determined by the structural parameters of the molecule. The nonzero asymmetry parameter η causes a complex structure of the singularities in the 2М correlation NMR and NQR spectra of powders. For a long time there has been no analytical method of determining these singularities in arbitrary cases.Brombacher [6] was the first to describe analytically the complex structure of the singularities in the 2М exchange NMR spectra of powders. Unfortunat...