  Cosmological implications of clusters of galaxies are discussed with
particular attention to their importance in probing the cosmological
parameters. More specifically we compute the number counts of clusters of
galaxies, Log $N$ -- Log $S$ relation, in X-ray and submm bands on the basis of
the Press--Schechter theory. We pay particular attention to a set of
theoretical models which well reproduce the {\it ROSAT} 0.5-2 keV band Log $N$
-- Log $S$, and explore possibilities to break the degeneracy among the viable
cosmological models.
