High spin states in123,124I were populated via the116Cd(11B,xn) reaction at 38 MeV bombarding energy and via the110Pd(18O,pxn) reaction at 75 MeV energy. γ-ray energies, intensities, γγ coincidences and DCO ratios were measured with the GASP spectrometer. The level schemes were extended considerably. Band terminations were observed in both nuclei. In123I the rotational band, which is built on the πh 11/2 single-particle state was extended to spinI π=(35/2)−; at higher spin the level spacings and the feeding pattern were found to become irregular, indicating a structure change. The (39/2)− state and the higher-lying (43/2)− level were interpreted as aligned oblate states. In124I a decoupled band was found to terminate in the same spin region. Total Routhian surface calculations were performed which support the occurrence of a band termination.