The nuclear magnetic shielding sigma in a molecule is changed by the presence of an external uniform electric field. This change may be expressed in terms of the shielding polarizabilities sigma' and sigma''. Values of sigma' and sigma'' have been evaluated for H-2, N2, HF and CO using a combination of the second order Moller-Plesset theory (MP2) and the finite-field perturbation theory. The effects of electron correlation on the sigma' and sigma'' tensors for N2, HF and CO are seen to be sufficiently large that a higher-order theory than MP2 will be necessary to account for them fully.