  The upper and the lower bounds of the lightest CP-even Higgs-boson mass
($m_h$) are discussed in the two-Higgs-doublet model (2HDM) with a
softly-broken discrete symmetry. They are obtained as a function of a cut-off
scale $\Lambda$ ($\leq 10^{19}$ GeV) by imposing the conditions in which the
running coupling constants neither blow up nor fall down below $\Lambda$. In
comparison with the standard model (SM), although the upper bound does not
change very much, the lower bound is considerably reduced. In the decoupling
regime where only one Higgs boson ($h$) becomes much lighter than the others,
the lower bound is given, for example, by about 100 GeV for $\Lambda = 10^{19}$
GeV and $m_t = 175$ GeV, which is smaller by about 40 GeV than the
corresponding lower bound in the SM. In generic cases, $m_h$ is no longer
bounded from below by these conditions. If we consider the $b \to s \gamma$
constraint, small values of $m_h$ are excluded in Model II of the 2HDM.
