A dispersion-theoretic approach is developed for systems with large binding energies. Strong binding can be obtained if the one-particle exchange force is singular at short distances. Many-meson exchange forces play an important role and are described by a suitable asymptotic expression. The method is used to construct a relativistic degenerate quark model of mesons. The model is unsatisfactory in the sense that, while yielding a sufficiently strong binding, the symmetry required for SU6-invariant vertices in the static limit is destroyed by the relativistic motion of the quarks. It is conjectured that a realistic quark model of mesons necessarily requires the existence of long-range, "superstrong" interactions.