We have investigated the effect of divalent Ca, Sr and Zn atoms at the Y, Ba and Cu sites, respectively, of the YBa 2Cu 3O 7− δ single crystal on the magnetoconductivity and magnetic irreversibility properties for H|| c axis and J|| ab plane. The resistive transition is a clear two-step process. While the upper temperature step is only weakly affected by low applied fields, the lower temperature step is visibly broadened and shifted down to lower temperatures. Between upper and lower temperature steps lays the magnetic irreversibility line, T irr( H) which follows the power law predicted by the flux creep theories in most of the high field range. However, in a low field region, the T irr( H) exhibits two different regimes dominated by disorder and frustration and characterized by the de Almeida–Thouless and Gabay–Toulouse power law behaviors. We attribute the origin of the observed stepwise resistive transition and low field magnetic irreversibility regimes mainly to the granularity of the superconducting state of our doped samples and contrast our magnetic irreversibility present results with those of a pure YBa 2Cu 3O 7− δ single crystal. We suggest that the valance as well as the local breaking of the orbital symmetry by impurities plays an important role in the induction of this state. On the other hand, our results show that granular superconductivity can be induced in the YBa 2Cu 3O 7− δ system by divalent impurities doping in whatever site Y, Ba or Cu.