  Possibility of a novel pseudo-scalar (octupole) order is studied
theoretically for orbitally degenerate systems with strong spin-orbit coupling
such as Ce$_x$La$_{1-x}$B$_6$. It is discussed that coexistence of an octupole
order parameter and antiferromagnetic fluctuation should lead to drastic
softening of the elastic constant by a mode-mixing effect. Nonlinear coupling
between dipole, quadrupole and octupole fluctuations is taken into account in
terms of a Ginzburg-Landau-type functional which is derived microscopically
through path integral.
