  We examine possibility of enhancement of superconductive critical temperature
in two-dimensions. The weak coupling BCS theory is applied, especially when the
Fermi level is near the edges of the electronic bands. The attractive
interaction depends on ${\bf k}$ due to screening. The density of states(DOS)
does not have a peak near the bottom of the band, but $k$-dependent
contribution to DOS (electron density on the Fermi surface) has a diverging
peak at the bottom or top. These features lead to significant enhancement of
the critical temperatures. The results are qualitatively consistent with the
superconductive behaviors of HfNCl ($\Tc \le 25K$) and ZrNCl($\Tc \le 15K$),
C$_{60}$ with a field-effect transistor configuration ($\Tc = 52K$), and
MgB$_2$ ($\Tc \approx 40K$) which have the unexpectedly high superconductive
critical transition temperatures.
