We report ab initio calculations of the indirect nuclear spin±spin coupling constants of PbH 4 using a basis set which was specially optimized for correlated calculations of spin±spin coupling constants. All nonrelativistic contributions and the most important part of the spin±orbit correction were evaluated at the level of the random phase approximation. Electron correlation corrections to the coupling constants were calculated with the multicon®gurational linear-response method using extended complete and restricted active space wavefunctions as well as with the second-order polarization propagator approximation and the second-order polarization propagator approximation with coupled-cluster singles and doubles amplitudes. The eects of nuclear motion were investigated by calculating the coupling constants as a function of the totally symmetric stretching coordinate. We ®nd that the Fermi contact term dominates the Pb·H coupling, whereas for the H·H coupling it is not more important than the orbital paramagnetic and diamagnetic contributions. Correlation aects mainly the Fermi contact term. Its contribution to the one-bond coupling constant is reduced by correlation, independent of the method used; however, the dierent correlated methods give ambiguous results for the Fermi contact contribution to the H·H couplings. The dependence of both coupling constants on the Pb·H bond length is dominated by the change in the Fermi contact term. The geometry dependence is, however, overestimated in the random phase approximation.