The study of thallium nonstoichiometry in the thallium 2212 cuprate by X-ray diffraction and electron microscopy has allowed a significant homogeneity range to be isolated, Tl{sub 2{minus}x}Ba{sub 2}CaCu{sub 2}O{sub 8{plus minus}{delta}} with 0{le}x{lt}0.4. The HREM study showed that thallium deficiency is not accommodated through an intergrowth mechanism but implies a statistical distribution of Tl atoms and vacancies in the thallium double layers. However, it appeared that modulated areas can arise from ions' and vacancies' local orderings in the (111) plane of the rock salt layers; they result in satellites in the E.D. patterns. The study of the superconducting properties of these oxides shows that the critical temperature is not greatly affected by the thallium nonstoichiometry, whereas hydrogen-argon annealings confirm the predominant role of oxygen non stoichiometry upon T{sub c}'s , allowing a (T{sub c}){sub R=0} of 120 K to be reached for x = 0.4. The deterioration of the grain boundaries by hydrogen annealing is also studied.