The total photoneutron cross sections for 58Ni and 60Ni have been measured with bremsstrahlung from threshold to 24 MeV. Although their magnitudes are greatly different, the two cross sections show similar structure over the giant dipole resonance region. The structural features of both are in only fair agreement with the dynamic collective model calculations of Huber, and of Seaborn, Drechsel, Arenhövel and Greiner. However the agreement of the 60Ni cross section and the collective correlations calculation of Seaborn et al. is far better, and thus indicates the importance of shell-model aspects.