Both, experimental and modelling evidence is presented in this study showing that interlayer anion exchange is the dominant sorption mechanism for iodide (I^-) on AFm phases. AFm phases are Ca-Al(Fe) based layered double hydroxides (LDH) known for their large potential for the immobilization of anionic radionuclides, such as dose-relevant iodine-129, emanating from low- and intermediate-level radioactive waste (L/ILW) repositories. Monosulfate, sulfide-AFm, hemicarbonate and monocarbonate are safety-relevant AFm phases, expected to be present in the cementitious near-field of such repositories. Their ability to bind I^- was investigated in a series of sorption and co-precipitation experiments. The sorption of I^- on different AFm phases was found to depend on the type of the interlayer anion. Sorption R_d values are very similar for monosulfate, sulfide-AFm and hemicarbonate. A slightly higher uptake occurs by AFm phases with a singly charged anion in the interlayer (HS-AFm) as compared to AFm with divalent ions (monosulfate), whereas uptake by hemicarbonate is intermediate. No significant sorption occurs onto monocarbonate. Our derived thermodynamic solid solution models reproduce the experimentally obtained sorption isotherms on HS-AFm, hemicarbonate and monosulfate, indicating that anion exchange in the interlayer is the dominant mechanism and that the contribution of I^- electrostatic surface sorption to the overall uptake is negligible.