The effects of a static uniform electric field on the NMR shielding and magnetizability of F2, HCN, HNC, HCCH, H2O, NH3, CH4, HCHO, and H2O2 are investigated. The quantities 2 3 4 which govern these effects are the shielding and magnetizability polarizabilities and these are calculated in a mixed numerical-analytical scheme at both the electron-uncorrelated and electron-correlated levels of theory. For the latter, correlation is introduced via second- or third-order Møller-Plesset theory or via linearized coupled cluster double excitation theory. This is the first time that these theories have been applied to these properties for these molecules. Furthermore, for F2, HNC, and H2O2 there have been no calculations of any kind before, and for NH3 and HCHO there have been no correlated calculations, for HCHO the magnetizability polarizability has not been determined previously. The investigation highlights the extreme difficulty, in most cases, of obtaining definitive values for these properties; this is especially true for F2 where electron correlation plays a dominant role. In general, electron correlation is much more important for the rotationally averaged shielding polarizabilities than for the magnetizability-polarizability anisotropy which governs the Cotton-Mouton effect.