The components of the tensors σ(1)and σ(2)which describe respectively the linear and quadratic electric field dependence of the nuclear magnetic shielding have been computed for the hydrogen molecule using SCF perturbation theory with an extended basis set which includes s-, p- and d-orbitals on both nuclei. The calculated components of σ(1)are only slightly affected by the incorporation of d-orbitals unlike those of σ(2)which are altered quite markedly. For the mean shielding the present results provide an interesting comparison with the results of other theoretical and experimental studies.