[en] A study of the beta decays of ¹²⁶Cd and ¹²⁶In using the TRISTAN on-line isotope separator facility is reported. Gamma-ray singles measurements were made for both decays usng Ge(Li) and LEPS (low energy photon spectrometer) detectors. In addition, gamma--gamma coincidence measurements and gamma multiscale measurements were made for both decays using Ge(Li) detectors. The half-life for ¹²⁶Cd was determined to be 0.506 +- 0.015 sec., and the half-lives for the low- and high-spin ¹²⁶In isomers were determined to be 1.83 +- 0.11 sec. and 1.96 +- 0.10 sec., respectively. A total of 11 gamma rays were observed in the decay of ¹²⁶Cd, and all but one were placed in a level scheme for ¹²⁶In. A total of 48 gamma rays were observed in the decay of the low- and high-spin ¹²⁶In isomers and all were placed in a level scheme for ¹²⁶Sn. Spin and parity assignments were deduced, whenever possible, on the basis of logft values and gamma decay selection rules. The ¹²⁶In decay schemes (one has been proposed for each isomer) are compared with earlier decay studies and with results from ¹²⁴Sn(t,p)¹²⁶Sn reaction experiments. The systematics associated with the level schemes are discussed and a comparison is made with the nuclear shell model. 49 references