The voltage-current (V-I) characteristics, critical temperatures and the critical currents of Tl2Ba2CaCu2O8 (Tl-2212) and Tl2Ba2Ca2Cu3O10 (Tl-2223) ceramic superconductors were studied in magnetic fields up to 80 mT after several gamma irradiations up to 100 MR. The effect of gamma irradiation on the structure of these materials has also been studied. The normal state resistance increases by 20-30% with gamma irradiation, most of the changes taking place in low gamma 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 gamma dose. For Tl-2212 in the 96-98 K temperature range the V-I behaviours become nearly ohmic under a gamma 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 gamma 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 gamma 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 gamma irradiation but substantial electronic excitations and point defects may be generated, at higher rate in low gamma doses, to affect the concentration and arrangements of the carriers and the links between the grains.