  In order to constrain parameters in galaxy formation theories, especially
those for a star formation process, we investigate cold gas in elliptical
galaxies. We calculate the detection rate of cold gas in them using a
semi-analytic model of galaxy formation and compare it with observations. We
show that the model with a long star formation time-scale (~20 Gyr) is
inconsistent with observations. Thus, some mechanisms of reducing the mass of
interstellar medium, such as the consumption of molecular gas by star formation
and/or reheating from supernovae, are certainly effective in galaxies. Our
model predicts that star formation induced when galaxies in a halo collide each
other reduces the cold gas left until the present. However, we find that the
reduction through random collisions of satellite (non-central) galaxies in mean
free time-scale in a halo is not required to explain the observations. This may
imply that the collisions and mergers between satellite galaxies do not occur
so often in clusters or that they do not stimulate the star formation activity
as much as the simple collision model we adopted. For cD galaxies, the
predicted detection rate of cold gas is consistent with observations as long as
the transformation of hot gas into cold gas is prevented in halos whose
circular velocities are larger than 500 km s^-1. Moreover, we find that the
cold gas brought into cDs through captures of gas-rich galaxies is little. We
also show that the fraction of galaxies with observable cold gas should be
small for cluster ellipticals in comparison with that for field ellipticals.
