  Elementary excitations in the multipole ordered state, which models the phase
III in CeB6, are investigated by means of a generalized Holstein-Primakoff
formalism. When different kinds of nearest-neighbor exchange interactions
between multipoles are comparable to each other, orbital-flip excitations
exhibit almost one-dimensional dispersion along the z axis. With high symmetry
of the interactions, zero modes appear due to the macroscopic degeneracy of the
ground state. The next-nearest-neighbor dipole-dipole interaction, which
stabilizes the magnetic order of the phase III in CeB6, lifts the degeneracy
and leads to gapfull excitation spectrum. When the octupole-octupole
next-nearest-neighbor interaction exists simultaneously, the spectrum shows
softening at \Gamma and Z points. These excitations may be probed by neutron
scattering and ultrasonic measurements.
