The paper describes a study of the antiferromagnetic ordering of oxygen-deficient Nd1 + yBa2 - yCu3O6 + x single crystals. In pure, stoichiometric samples, y = 0, with different oxygen contents x in the Cu(1) plane (0.02<x<0.2), the antiferromagnetic I (AFI) phase appears to be stable down to 316 mK. The magnetic ordering within the Cu(2) sublattice of the pure NdBa2Cu3O6 + x system is therefore similar to that of the pure YBa2Cu3O6 + x parent compound. With increasing oxygen content, the Neel temperature drops significantly and the critical exponent changes from 0.26 for NdBa2Cu3O6.09 to about 0.5 for NdBa2Cu3O6.23. Magnetic ordering of the Nd3+ moments sets in at 1.7 K with a critical wave vector q(Nd) = (1/2 1/2 1/2). Reordering to the AFII phase is observed in a crystal, which has a significant amount (4%) of Nd3+ ions substituted on the Ba sites. The relatively high temperature T-2=95 K of this reordering suggests that the Nd3+ ions on Ba sites are very effective defects forcing the AFI<->AFII reordering. The mechanism of reordering is explained in terms of the creation of Cu2+ moments within the Cu(1) layer due to the Nd3+ ions on Ba sites, which via polarization lead to an effective ferromagnetic coupling between the moments on next-nearest neighboring Cu(2) layers. The Nd3+ doping on the Ba2+ sites increases the Neel temperature compared to the stoichiometric compound.