The theory of multiband superconducting systems with variable density of charge carriers is analyzed. The possibility of emergence of nonphonon high-temperature superconductivity due to the predominance of electron–electron interband interactions over intraband interactions, as well as due to the fact that the thermodynamic and magnetic properties of multiband systems in the superconducting phase differ qualitatively from those of single-band systems, is indicated. Phase transitions in a quasi-2D anisotropic medium upon a change in the carrier concentration, i.e., a transition from the commensurate to the incommensurate state of the spin density wave, are analyzed. Such a transition is observed when the Umklapp processes in the lattice structure are taken into account. These processes facilitate a deviation of wavevector Q of the spin density wave from 2k_F, as well as a displacement of the bandgap relative to the Fermi surface. This leads to the generation of free charge carriers and the possibility of superconductivity. It is shown that superconductivity accompanies the magnetism. The conditions for the coexistence of these two phenomena are determined.