The voltage-current (V -I ) characteristics, critical temperatures and the critical currents of Tl 2 Ba 2 CaCu 2 O 8 (Tl-2212) and Tl 2 Ba 2 Ca 2 Cu 3 O 10 (Tl-2223) ceramic superconductors were studied in magnetic fields up to 80 mT after several γ irradiations up to 100 MR. The effect of γ irradiation on the structure of these materials has also been studied. The normal state resistance increases by 20-30% with γ irradiation, most of the changes taking place in low γ doses up to 10 MR. The critical temperatures of Tl-2212 and Tl-2223 decrease by about 8 K up to 30 MR and approach the saturation values of 101 K and 113 K, respectively, with further increase of γ dose. For Tl-2212 in the 96-98 K temperature range the V -I behaviours become nearly ohmic under a γ dose of about 30 MR or in an external magnetic field of 20-30 mT. In the same temperature range the critical current decreases rapidly in low γ doses up to 10-25 MR; above that it decreases only slightly. For both materials, the positions and widths of the x-ray diffraction peaks almost remain the same but the peak intensities decrease by 10-40% with γ irradiation, the rate of decrease being higher in the 0-30 MR range. These observations indicate that drastic changes in the lattice do not take place with γ irradiation but substantial electronic excitations and point defects may be generated, at higher rate in low γ doses, to affect the concentration and arrangements of the carriers and the links between the grains.