The statistical bootstrap model (SBM) is extended to describe hadronic systems which carry the quantum number of strangeness. The study is conducted in the three-dimensional space $(T,{\mu }_q,{\mu }_s)$ of temperature, up-down, and strange chemical potentials, respectively, wherein the existence of a “critical” surface is established, which sets the limits of the hadronic phase of matter. A second surface, defined by the null expectation value of strangeness number $(〈S〉=0)$ is also determined. The approach of the latter surface to the critical one becomes the focal point of the present considerations. Two different versions of the extended SBM are examined, corresponding to the values 2 and 4 for the exponent α, which determines the asymptotic falloff of the mass spectrum $\rho \mathrm{}\left(m\right).$ It is found that the $\alpha =4\mathrm{}$ version has decisive physical advantages. This model is subsequently adopted to discuss (strange) particle ratios pertaining to multiparticle production processes, for which a thermal equilibrium mode of description applies.

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