The irreversibility line in the H–T plane divides the irreversible and reversible behaviour of the magnetization which is of importance for the characterization of high Tc superconductors. In this work, we report the production of Y1–XLuXBa2Cu3O7–δ (X=0.4, 0.5 and 0.6) superconducting system using the usual solid state reaction method. The irreversibility line H–T plane for the Y1–XLuXBa2Cu3O7–δ polycrystalline sample was investigated. The curves of magnetization ZFC (cero field cooled)- FC (field cooled) were measured in magnetic fields between 100 Oe and 4000 Oe, and allowed to obtain the values for irreversibility and critical temperatures.