The geometric derivatives of the static and dynamic electric dipole polarizability have been calculated at the all-electron Dirac-Hartree-Fock level for the dihalogen molecules F-2, Cl-2, Br-2, and I-2 and for the hydrogen halides HF, HCl, HBr, and HI. A comparison with the non-relativistic Hartree-Fock values shows that the relativistic corrections tend to be larger for the geometric derivatives of the polarizabilities than for the polarizabilities. The frequency dispersion of the corrections due to relativity is significant for the molecules containing bromine and iodine. As expected, for the same molecules relativistic effects are sizable, and they improve the agreement between theory and experiment for the electric dipole polarizabilities. In the case of the Raman scattering cross sections, only a few experimental data are available. In general the relativistic effects are in this case within the range of the experimental error. (C) 2003 Elsevier Science B.V. All rights reserved.