  In this work, results of {\it ab-initio} band structure calculations for
$A_2BC$ Heusler compounds that have $A$ and $B$ sites occupied by transition
metals and $C$ by a main group element are presented. This class of materials
includes some interesting half-metallic and ferromagnetic properties. The
calculations have been performed in order to understand the properties of the
minority band gap and the peculiar magnetic behavior found in these materials.
Among the interesting aspects of the electronic structure of the materials are
the contributions from both $A$ and $B$ atoms to states near the Fermi energy
and to the total magnetic moment. The magnitude of the total magnetic moment,
which depends as well on the kind of $C$ atoms, shows a trend consistent with
the Slater-Pauling type behavior in several classes of these compounds. The
localized moment in these magnetic compounds resides at the $B$ site. Other
than in the classical Cu$_2$-based Heusler compounds, the $A$ atoms in Co$_2$,
Fe$_2$, and Mn$_2$ based compounds may contribute pronounced to the total
magnetic moment.
