A theory of multiple quantum (MQ) NMR dynamics is developed for systems of interacting equivalent spins (s=1/2). The theory can be applied for the interpretation of both MQ NMR spectra of bullvalene molecules dissolved in nematic liquid crystal solution and MQ NMR of nanopores in an external magnetic field. Numerical realization of the developed approach allows us to investigate MQ NMR dynamics in systems consisting of several hundred spins. The dependence of the MQ NMR coherence intensities on their orders (the profile of MQ coherence) is investigated in many-spin systems. It is shown that the profile is exponential in such systems. We discuss the information which can be extracted from MQ NMR spectra of systems of interacting equivalent spins.

We present some new results based on the relaxation function theory for a doped two-dimensional Heisenberg antiferromagnetic system with damping of paramagnon-like excitations. The Lorentzian form for the imaginary part of the dynamic spin susceptibility gives a reasonable agreement with neutron scattering and plane copper nuclear spin-lattice relaxation rate ⁶³(1/T₁) data in right up to optimally doped La_2-xSr_xCuO₄.

For the first time the inverse Laplace transform was applied for analysis of ³He relaxation in porous media. It was shown that inverse Laplace transform gives new information about these systems. The uniform-penalty algorithm has been performed to obtain the ³He relaxation times distribution in pores of clay sample. It is possible to obtain pores' sizes distribution by using applicable model.