Excited states of fundamental particles in some models of quantum field theory

An idea that the experimentally-observed meson resonances are excited states of fundamental mesons is presented, and is tested for several models of quantum field theory. It is shown that in the considered models, the excited states of mesons do exist and form infinite trajectories in the plane mass square-spin: these trajectories are either linear for all J or approximately linear for small J >= 7, depending on the form of the interaction Lagrangian. (orig.)