<p>The irreversibility properties of High-Tc superconductors are of major importance&nbsp;for technological applications. For example, a high irreversibility magnetic&nbsp;field is a more desirable quality for a superconductor (Viera, et al., 2001).&nbsp;The irreversibility line in the H-T plane is constituted by experimental points,&nbsp;which divides the irreversible and reversible behavior of the magnetization.&nbsp;The irreversibility lines for series of Lu1Gd2Ba5Cu8O18 and Lu 1.5&nbsp;Gd Ba Cu O polycrystalline samples with different doping were investi- 1.5 5 8 18&nbsp;gated. The samples were synthesized using the usual solid estate reaction&nbsp;method. Curves of magnetization ZFC (Zero Field Cooled) FC (Field Cooled)&nbsp;for the system Lu Gd Ba Cu O and Lu Gd Ba Cu O , were measured in 1 2 5 8 18 1.5 1.5 5 8 18&nbsp;magnetic fields of the 100 to 2,000 Oe, and allowed to obtain the values for the&nbsp;irreversibility and critical temperatures. The data of irreversibility temperature&nbsp;allowed demarcating the irreversibility line, T H). Two main lines are used for irr(the interpretation of the irreversibility line: one of those which suppose that the&nbsp;vortexes are activated thermally and the other proposes that associated to Tirr<br>(Irreversibility Temperature) a phase transition occurs. The irreversibility line is&nbsp;described by a power law. The obtained results allow concluding that in the&nbsp;system Lu Gd Ba Cu O and Lu Gd Ba Cu O a characteristic bend of the 1 2 5 8 18 1.5 1.5 5 8 18&nbsp;Almeida-Thouless (AT) tendency is dominant for low fields and a Gabay-&nbsp;Toulouse (GT) behavior for high magnetic fields.</p>