A semiclassical calculation of the particle spectrum in the Gross--Neveu model was carried out. It is a two-dimensional model with N species of fermions interacting through a symmetrical scalar-scalar interaction and is renormalizable, asymptotically free, and exhibits spontaneous symmetry breaking. A rich spectrum of particles is found which can be interpreted as fermion- antifermion bound states and multifermion bound states. These states fall into supermultiplets whose origin one does not completely understand. The binding mechanism is a vacuum-polarization effect rather than the direct interaction between particles. A general method for handling fermions in semiclassical calculations is developed. (auth)