Considerations are given to the possibility that the selfconsistency requirements of some dispersion-theoretic bootstrap model may specify uniquely the set of strongly interacting particles found in nature. The discussion is based on a particular, approximate model of the P (pseudoscalar) and V (vector) mesons. In this model the V exchange forces in the P + P states produce the V mesons, and the V exchange forces in the P + V states produce the P mesons. Attention is limited to systems in which the particles arising in a particular way are degenerate or nearly degenerate, and are represented by a small number of irreducible representations of a simple Lie group of first, second, or third rank. Three plausible self-consistency requirements are postulated. The smallest meson set thnt sntisfies all three postulates corresponds to the group SU/sub 3/. The predicted particles in this scheme are a P-meson octet, a V octet, a V singlet, and a singlet particle of spin and parity 2/sup -/. One of the self-consistency postulates is concerned with deviations from degeneracy, and leads to the Gell- Mann-Okubo sum rule for the SU/sub 3/ scheme. The double septet scheme of the group G/sub 2/ does not satisfy anymore » of the postulates. (auth)« less