  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 of temperature, up-down and strange chemical
potentials, 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 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, which
determines the asymptotic fall-off of the mass spectrum. It is found that the
version with the value 4 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.
