The relativistic mass correction contributions to the nuclear magnetic shielding sigma(MC)(X) within the polarization propagator approach both at the pure zeroth-order (PZOA) and at the random phase approximation (RPA) were calculated for the heavy atoms X of a series of hydrides XHn (n = 1-3). Inclusion of sigma(MC)(X) brings the non relativistic nuclear magnetic shieldings to agreement with fully relativistic four-component calculations, as noted previously for the hydrogen halides. The analysis in terms of contributions from localized orbitals shows that this contribution has an inner core origin, while it remains unaffected by excitations involving bonding orbitals and lone pairs. For all the compounds studied, sigma(PZOA)(MC)(X) differs from sigma(RPA)(MC)(X) in less than 5%, although at a much lower computational cost. (C) 2002 Elsevier Science B.V. All rights reserved.