A number of problems involving the spectrum of elementary excitations of superfluid Fermi systems were studied by the methods of quantum field theory. A system with direct binary interaction is considered at zero and non-zero temperature, as well as an electron-phonon system at absolute zero. On finding Schwinger's equations for oneparticle Greene functions, use was made of the ground state approximation proposed by N. N. Bogoliubov, i.e., a formalism was applied which does not preserve the full number of particles. (auth)