We investigate the relativistic effects on the electric field gradient (EFG) at the nucleus, the generalized Stemheimer shielding constants, and the EFG polarizabilities using analytic quadratic response theory at the four-component Dirac-Hartree-Fock level of theory. Particular attention is paid to the basis set requirements for calculations at the four-component level of theory of these higher-order properties involving operators that probe both the near-nucleus and the outer regions of the electron density. Our results show that relativistic effects become non-negligible for the hydrogen halides starting with hydrogen bromide and the heavier members of the group 17 halides. Interestingly, the relativistic effects are much more pronounced for the heavy-atom in hydrogen bromide, being about 10% for most of the generalized EFG polarizabilities, than in the homonuclear diatomic molecule Br2, where relativistic effects in general are much less than 10%. © 2003 Elsevier B.V. All rights reserved.