  Correlation between orbital structure and magnetic ordering in bilayered
manganites is examined. A level separation between the $3d_{3z^2-r^2}$ and
$3d_{x^2-y^2}$ orbitals in a Mn ion is calculated in the ionic model for a
large number of the compounds. It is found that the relative stability of the
orbitals dominates the magnetic transition temperatures as well as the magnetic
structures. A mechanism of the correlation between orbital and magnetism is
investigated based on the theoretical model with the two $e_g$ orbitals under
strong electron correlation.
