  The electronic structures of BaAlGe and SrAlGe which are superconductors with
hexagonal honeycomb layers have been studied by using a first principles
method. Energy bands, Fermi surafces, and density of states are presented. The
two materials have topologically different Fermi surfaces. BaAlGe has two Fermi
surfaces: One has a three dimensional spinning-top-like shape and the other has
a cylindrical shape with two dimensional character. SrAlGe has only one
connected Fermi surface. Two gap superconductivity for BaAlGe is suggested from
the inherently different character of the two Fermi surfaces. The higher $T_c$
of SrAlGe than BaAlGe is related to the difference in both the topology of the
Fermi surface and the band dispersions along the $z$ direction.
