Composite and elementary particles with the same quantum numbers in quantum field theory

The formal framework of a theory containing $N$ elementary particles with the same quantum numbers is described. It is shown that the proper mass of the elementary particles must have poles if composite particles with the same quantum numbers can be formed. Equations are written down that determine the parameters of a composite particle. The symmetry of these equations under permutations of the parameters of the composite particle and any one of the elementary particles is discussed; this symmetry does not, however, always imply physical equivalence of these particles. Another problem investigated is the possibility of describing the composite particles in such a theory as a special case of elementary particles of a different theory. Conditions of nonelementarity are formulated; these transform $M$ of $N+M$ particles with identical quantum numbers into composite particles.