  We obtain the hadronic mass spectrum in the `bag of bags' statistical
bootstrap model (BBSBM), implementing the colorless state condition, aside of
baryon and strangeness conservation, using group projection method. We study
the partition function, investigate the properties of dense hadronic matter,
and determine the conditions under which the system undergoes a phase
transition to a deconfined quark-gluon plasma. We show that a phase transition
cannot occur in the N=1 (Abelian) limit of our model, and is first order for
QCD-like case N=3.
