Quasirelativistic theory of magnetic shielding constants based on the Douglas-Kroll-Hess transformation of the magnetic potential presented in a previous paper is extended to molecular systems that contain heavy elements. The gauge-including atomic orbital method is adapted to the quasirelativistic Hamiltonian to allow origin-independent calculations. The present theory is applied to the proton and halogen magnetic shielding constants of hydrogen halides and the Hg-199 magnetic shielding constants and chemical shifts of mercury dihalides and methyl mercury halides. While the relativistic correction to the magnetic interaction term has little effect on the proton magnetic shielding constants, this correction is a dominant origin of the heavy atom shifts of the magnetic shielding constants of heavy halogens and mercury. The basis set-dependence of mercury shielding constants is quite large in the relativistic calculation; it is important to use the basis functions that are optimized by the relativistic method to properly describe the relativistic effect. The relativistic correction to the magnetic interaction term is quite important for mercury dihalides in which the relativistic effects from mercury and halogen are strongly coupled. Without this correction, we obtain quite incorrect results. The origin of the Hg-199 chemical shifts in mercury dihalides is the spin-orbit interaction from heavy halogens. In methyl mercury halides, the paramagnetic shielding term as well as the spin-orbit interaction from heavy halogens dominates the Hg-199 chemical shifts. (C) 2003 American Institute of Physics.