  The mean-field theory with the use of the slave-boson functional method is
generalized to take account of the spin- and orbital-ordered state in the
doubly degenerate Hubbard model. Some numerical calculations are presented of
the antiferromagnetic orbital-ordered state in the half-filled simple-cubic
model. The orbital order in the present theory is much reduced compared with
that in the Hartree-Fock approximation because of the large orbital
fluctuations. From a comparison of the ground-state energy, the
antiferromagnetic orbital state is shown to be unstable against the
antiferromagnetic spin state, although the situation becomes reversed when the
exchange interaction is {\it negative}.
