The quadrupole moments (Qo) of the highly deformed, second minimum bands in '33Nd and " Nd have been extracted from mean lifetime measurements using the Doppler shift attenuation method. The reactions ' 'Pd("S, 2p2n )'"Nd at 152 MeV and ' Ru(' S, 3n)" Nd at 145 MeV were used. A standard centroid shift analysis was carried out in both cases, which gave values of Qo=(6.0+0.7)eb and (4.0+0.5)e b for '33Nd and "~Nd, respectively, corresponding to axial prolate deformations of P2--0.33 and =0.22. A line-shape analysis was also carried out for '"Nd to check against the possible effect of sidefeediug. The result was Qo=(6.7+0.7)eb, with sightly slower sidefeediug times corresponding to Q, &--5.3e b. The results are in good agreement with the predictions of total Routhian surface calculations, and are discussed in the context of other highly deformed bands in the A = 130 -140 mass region.