A rotational band with K 7 * -0 + with 7=0 and I = 2 at excitation energies of 1410.8 and 1438.5 keV, respectively, has been identified and carefully characterized in 240 Pu. We conclude that these states are members of a two-phonon octupole vibrational band.Rotational energy bands of collective character based on surface vibrations are predicted within the framework of the Bohr-Mottelson model 1 for nuclei with large equilibrium deformation. The one-phonon collective vibrations, l#co x , of the quadrupole type, A = 2, and of the octupole type, A = 3, are well established in both deformed and spherical nuclei 2 and the two-phonon shape vibrational states of the quadrupole type, 2H(JO 2 , have been identified in many spherical nuclei. 2 Meyer 3 has recently suggested the existence of a coupled /3-y vibrational mode with two-phonon character in 154 Gd.However, no states in either spherical or deformed nuclei have been identified thus far that possess two-phonon octupole vibrational characteristics. Unseccessful attempts to identify these two-phonon octupole vibrations, 2^co 3 , in the heavy-mass deformed region have been made by Bj^rnholm. 4 Since the lowest frequencies of the collective octupole vibration, co 3 , occur in this mass region (220 < A 5250), the possibility that these states can be populated in radioactive decay is much larger than for spherical nuclei or for the rare-earth deformed nuclei.We have identified a collective rotational band in 240 Pu, populated in the p~ decay of 240m Np, which we suggest is the two-phonon octupole vibration. This is the first such identification of this class of shape vibrations in nuclei and is only the second case of established two-quantum vibrations of any type for nuclei with large equilibrium deformation.Energy levels in 240 Pu have been investigated by observing the gamma rays following the j3~ decay of the 7.4-min isomer of 240 Np with lithiumdrifted germanium detectors, Ge(Li). We have used a source consisting of 15.3 mg of 8.28 x 10 7 -yr 244 Pu, electromagnetically enriched to 99.1% in mass 244, as the equilibrium grandparent activity for 240m Np. Extensive gamma-gamma coincidence measurements and some directional correlation experiments using Ge(Li)-NaI(Tl) detectors have been performed in order to elucidate the decay scheme. A preliminary report on some of these experiments has been presented 5 and a more complete description including the isomers of 240 Np and the alpha decay of 244 Cm to states in 240 Pu is the subject of a future publication. 6 A summary of some of the most prominent features of the energy levels in 240 Pu following the decay of 7.4-min 240m Np with assignments K*I = 0~1 is presented in the partial level scheme in Fig. 1. About one third of the observed gammaray transitions are shown here. In addition to the K = 0 ground-state rotational band with spin members 0 + , 2 + , 4 + , and 6 + , a well established K = 0 negative-parity band with/ 77 = 1", 3~, and 5"" is shown. The reduced intensity ratios for the El transitions depopulating the 1...