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The problem of the mass spectrum of mesons is considered from the oint of view of algebraic models based on the Lie algebras of non-compact groups. After describing the group-theoretical approach to particle physics and difficulties encountered in applying it to the mass spectrum problems, especially the O'Raifeartaigh-Segal-Jost theorems, we consider the class of algebraic models recently set forth by A. Bohm. These models emply the Lie algebras of certain, physically interesting Lie groups, but go outside the Lie algebraic structure by allowing non-Lie algebraic "coupling" terms. The resulting associative algebraic models can be given a rigorous foundation as an algebra of continuous operators on a rigged Hilbert space and mass formals can be derived.