An eigenvalue equation for the spectrum of lepton and quark is obtained from a truncated set of Tamm-Dancoff integral equations, generated by a four-fermion interaction based on a finite nonlocal quantum field theory. Eigenvalue equations for the meson and baryon mass spectra are also derived and integral equations are proposed for the scattering amplitudes, which can be used to calculate coupling constants in the nonlocal version of the standard model.