The density of hardron levels $\rho \mathrm{}\left(m\right)\mathrm{}$ has been derived from the statistical bootstrap model to have the asymptotic form $\rho \mathrm{}\left(m\right)\mathrm{}\sim c{m}^a{e}^{\mathrm{bm}}$ with $a\le -\frac{5}{2}$. We study the properties of ultradense hadronic matter characterized by level densities of this type. If $a<-\frac{5}{2}$ (as is preferred by the bootstrap model), we show that hadronic matter may be thermodynamically unstable at high densities. This instability is characterized by macroscopic fluctuations of the energy density and the existence of a negative specific heat. Implications of the instability are discussed with reference to high-energy collisions and astrophysics.

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