Voltage-current (V-I) characteristics of the ceramic Tl2Ba2CaCu2O8 (Tl-2212) and Tl2Ba2Ca2Cu3O10 (Tl-2223) superconductors were studied in magnetic fields up to 80 mT at different temperatures just below the critical temperature. The V-I data were fitted to a power law expression V = I-beta(T,I-B) in which the exponential parameter beta is found to decrease rapidly with increase of temperature and magnetic field. In zero magnetic field the slopes of beta versus T graphs change drastically in a narrow temperature range in which beta decreases from about 3 to about 2. At temperatures below about 0.8-0.9 T-c the critical current I-c rapidly decreases with magnetic fields up to about 20 mT. This is followed by a more gradual change up to about 60 mT before I-c decreases rapidly to zero in magnetic fields higher than 60 mT. These features of the Tl-based ceramic superconductors are quite similar to those of superconducting tapes. We propose that the lattice anisotropy, preferred orientation and behaviours of the weak and strong links between the grains play an important role in this similarity.