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A new method for relativistically corrected nuclear magnetic resonance (NMR) chemical shifts is developed by combining the individual gauge for the localized orbital approach for density functional theory with the normalized elimination of a small component using an effective potential. The new method is used for the calculation of the NMR chemical shifts of [SUP95]Mo and [SUP183]W in various molybdenum and tungsten compounds. It is shown that quasirelativistic corrections lead to an average improvement of calculated NMR chemical shift values by 300 and 120 ppm in the case of [SUP95]Mo and [SUP183]W, respectively, which is mainly due to improvements in the paramagnetic contributions. The relationship between electronic structure of a molecule and the relativistic paramagnetic corrections is discussed. Relativistic effects for the diamagnetic part of the magnetic shielding caused by a relativistic contraction of the s,p orbitals in the core region concern only the shielding values, however, have little consequence for the shift values because of the large independence from electronic structure and a cancellation of these effects in the shift values. It is shown that the relativistic corrections can be improved by level shift operators and a B3LYP hybrid functional, for which Hartree-Fock exchange is reduced to 15%. [ABSTRACT FROM AUTHOR]