Exchange resonance spectra of three sandwich devices containing nanolayers of Cr, Mn, Co, Ni, and Eu were recorded at 77 K. We found that these spectra are significantly different from those obtained earlier for Fe-SiO2-Au three-layer nanosandwich device. Detailed theoretical approach was developed to analyze the recorded spectra, g-factor values, and relaxation properties of the spin-polarized states in the nanolayers. We found that the g-factor values and spin-lattice relaxation rates may be adequately described by the spin-orbit scattering mechanism. Electric charge density fluctuations may also contribute to spin-lattice relaxation in nanolayers. Second-order effects in the relaxation mechanism were also briefly considered.