  In order to investigate multipole ordering in f-electron systems from a
microscopic viewpoint, we study the so-called \Gamma_8 models on three kinds of
lattices, simple cubic (sc), bcc, and fcc, based on a j-j coupling scheme with
f-electron hopping integrals through (ff\sigma) bonding. From the \Gamma_8
model, we derive an effective model for each lattice structure by using the
second-order perturbation theory with respect to (ff\sigma). By further
applying mean-field theory to the effective model, we find a \Gamma_{3g}
antiferro-quadrupole transition for the sc lattice, a \Gamma_{2u}
antiferro-octupole transition for the bcc lattice, and a longitudinal triple-q
\Gamma_{5u} octupole transition for the fcc lattice.
