The existence of a nuclear electric octupole moment (EOM) requires bot
h parity and time invariance violation. The EOM's of odd Z nuclei that
are induced by a particular T-and P-odd interaction are calculated. W
e compare such octupole moments with the collective EOM's that can occ
ur in nuclei having a static octupole deformation. A nuclear EOM can i
nduce a parity-and time-invariance-violating atomic electric dipole mo
ment, and the magnitude of this effect is calculated. The contribution
of a nuclear EOM to such a dipole moment is found, in most cases, to
be smaller than that of other mechanisms of atomic electric dipole mom
ent production.