The superconducting properties of the thallium cuprates, and especially their critical temperatures, are strongly affected by annealings in various gaseous atmospheres (nitrogen, oxygen, argon and hydrogen). These annealing effects have been studied for Tl2Ba2CaCu2O8, TlBa2CaCu2O7, TlBa2Ca2Cu3O9 and Tl2Ba2Ca2Cu3O10 as well as for the substituted oxides TlBa2Ca1-xLnxCu2O7 and Tl2Ba2Ca1-xLnxCu2O8 (Ln=Y, Nd). It is demonstrated that a drastic increase of Tc can be obtained, due to a very small oxygen deficiency. The most spectacular effect is obtained with a gas mixture H2/Ar, which can be performed at a temperature as low as 300°C, leading for example for the 2212 phase to an increase of Tc from 97 K to 118 K (to be compared to 125 K for the 2223 phase). Moreover it is shown by electron microscopy that at this annealing temperature the crystal remains unchanged. However, thermal treatments at 400°C or beyond alter the crystals in connection with a slight volatilization of thallium oxide. This dramatic effect of oxygen nonstoichiometry upon Tc decreses as the number m of copper layers in the perovskite slabs of the superconductors TlBa2Cam-1CumO2m+3 and Tl2Ba2Cam-1CumO2m+4 increses. These results show that the important factor which governs Tc in the thallium cuprates is the hole number per mole of copper in the structure and that this factor seems to be predominant with respect to the number m of copper layers. © 1990.