Anomalous NMR spectra in phases III and III' of CeB6 are analyzed theoretic
ally Ly introducing a new type of hyperfine coupling of the B-11 nuclei wit
h Ce multipolar moments. It is shown that the observed spectra can be repro
duced if we take into account the antiferro-polarization of the T-xyz octup
ole in addition to the antiferromagnetic order proposed by neutron diffract
ion experiment (ND). Thus ND and NMR are mutually consistent in phase III,
if the octupolar contribution is properly included. The analysis of NMR giv
es the magnitude of the polarization of the octupolar moment. The present a
nalysis strongly suggests that the antiferro-quadrupolar ordering of Gamma(
5)(+) type is playing an important role behind the mysterious 2k antiferrom
agnetic ordering of phase III.