The directional distributions of gamma rays from oriented nuclei have been used to study the level structures of 132 Xe and 154Gd populated following the decays of 132 I and 154 Eu respectively. The orientation was produced by using the hyperfine field in iron to polarize the spin system of nuclei at a temperature of 15 mK. The low temperature was achieved using a 3He 4He dilution refrigerator. The directional distribution of gamma rays were measured by a high resolution Ge(Li) detector. With these measurements unique spin assignments were made for most of the levels below 3 MeV in 132Xe. The multipole mixing ratios of 28 transitions in 132 Xe and 15 transitions in 154Gd are given. The results have been compared with the predictions based on the generalized collective model of Gneuss and Greiner and with the SU(5), SU(3) and 0(6) groups of the interacting boson approximation (IBA) model and the w dynamic deformation theory based on the pairing plus quadrupole model.