The level structure of the Balachandran generalization of the $N$-point Veneziano model is considered. The model is shown to exhibit consistent factorization and level structure. Using the harmonic oscillator formalism, expressions are obtained for the vertices coupling one or two excited states to any number of ground-state particles. The form of the propagator is also obtained. Both vertices and propagators are seen to reduce to the Veneziano form when an appropriate limit is taken. Asymptotically, the degeneracy of the $n$th level is shown to behave like exp (const $n^{\frac{2}{3}}$) where the constant is given explicitly. The Gross model of $N$-point functions is seen to exhibit a similar asymptotic degeneracy, in contradiction to other results reported in the recent literature.

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