[en] A study of the gamma-ray de-excitation following the beta decay of ¹³⁶I, ¹³⁸I and ¹³⁷Xe using the TRISTAN on-line isotope separator facility is reported. Gamma-ray singles and gamma-gamma coincidence measurements were made for all three decays using Ge(Li) detectors. In addition, gamma-ray multiscale measurements were made for the decay of ¹³⁶I. A total of 142 gamma rays were observed in the decay of the 45-and 85-second isomers of ¹³⁶I. Of these 115 were placed in a level scheme for ¹³⁶Xe consisting of 50 excited states up to 6624 keV. A total of 8 gamma rays were assigned to the decay of ¹³⁸I all of which were placed in a level scheme for ¹³⁸Xe consisting of 6 excited states at 589, 1073, 1464, 1867, 1903, and 2398 keV. Of the 94 gamma rays observed in the decay of ¹³⁷Xe, 83 were placed in a level scheme for ¹³⁷Cs consisting of 34 excited states up to 3976 keV. Gamma-ray multiscale measurements confirmed that ¹³⁶I has only two isomers. The half-life values obtained were 44.8 +- 1.0 and 85.2 +- 1.8 seconds. Spin and parity assignments were deduced, whenever possible, on the basis of gamma-ray transition probabilities and beta transition log ft values. The ¹³⁶I and ¹³⁷Xe decay schemes are compared with earlier decay studies and with results from (p,p') and proton transfer experiments. A possible correspondence of levels strongly populated by beta decay with neutron particle-hole states observed in (p,p') experiments is noted for ¹³⁶I levels around 4 MeV. The systematics associated with these level schemes are discussed and a comparison is made with recent shell-model calculations