  We extend the Statistical Bootstrap Model (SBM) in order to describe hadronic
systems which carry strangeness. We establish that the hadronic phase can exist
only in a region of the three-dimensional space of temperature, up-down and
strange chemical potentials, which is bounded by a critical critical surface.
We first employ the usual version of the SBM, which corresponds to the value 2
of the exponent which determines the asymptotic fall-off of the mass spectrum
and impose strangeness neutrality in order to obtain the relation between the
temperature and the chemical potentials of the quarks. We find an unphysical
behaviour of the strange chemical potential near the critical surface.
Subsequently, we study another version of SBM where the value of the exponent
equals 4 and we are led to a realistic as well as acceptable behaviour. In this
case we are also able to relate the parameter of the model, the critical
temperature at zero strange chemical potential) with the MIT bag constant B.
