  We consider the problem of the characteristics of mass spectra in the doubly
symmetric theory of fields transforming under the proper Lorentz group
representations decomposable into an infinite direct sum of finite-dimensional
irreducible representations. We show that there exists a range of free
parameters of the theory where the mass spectra of fermions are quite
satisfactory from the physical standpoint and correspond to the picture
expected in the parton model of hadrons.
