Fully relativistic calculations of the isotropic and anisotropic parts of both indirect nuclear spin-spin couplings (1)J(X-H) and (2)J(H-H) and nuclear magnetic shieldings sigma(X) and sigma(H) for the group-15 and -16 hydrides are presented. Relativistic calculations were performed with Dirac-Fock wave functions and the random phase approximation method. Results are compared to its nonrelativistic counterpart. Paramagnetic and diamagnetic contributions to the nuclear magnetic shielding constants are also reported. We found very large relativistic corrections to both properties in the sixth-row hydrides (BiH3 and PoH2). Our calculations of the relativistic corrections to the isotropic part of sigma at the heavy nucleus X show that it is roughly proportional to Z(3.2) in both series of molecules. Paramagnetic term sigma(p) is more sensitive to the effects of relativity than the diamagnetic one sigma(d), even though both have a behavior proportional to third power of the nuclear charge Z.