In the present study, one-bond P-31,P-31 indirect nuclear spin-spin coupling tensors, (1)J(P-31,P-31), are calculated using nonrelativistic and relativistic zeroth-order regular approximation (ZORA) density functional theory (DFT) methods for the following model molecules and ions: P-2, cis-MeP=PMe, trans-RP=PR (R = H, Me, Ph), (cis-eta(1)-PhP=PPh)Cr(CO)(5), (cis- and trans-eta(1)-MeP=PMe)Cr(CO)(5), H2P-PH2, H2P-PF2, cis- and trans-diphosphetes, a phosphole tetramer, [O3P-PO3](4-), [HO3P-PO3H](2-), [FO2P-PO2F](2-), Me-2(S)P-P(S)Me-2, [MeNequivalent toP-PMe3](+), and Me3P-PF5. These compounds have been chosen because the values of (1)J(P-31,P-31)(iso) in these systems vary from approximately -480 to +770 Hz, thereby spanning the known range of experimentally measured one-bond P-31,P-31 indirect nuclear spin-spin coupling constants. However, in many cases, the sign of (1)J(P-31,P-31)(iso) has not been determined by experiment. Our DFT results for (1)J(P-31,P-31)(iso) and the anisotropy of J are in qualitative agreement with experimental values; furthermore, our calculations provide the absolute sign of (1)J(P-31,P-31)(iso) in cases where it is unknown experimentally. A number of empirical trends between (1)J(P-31,P-31)(iso) and various structural parameters have been reproduced by our calculations. Inspection of the mechanisms which contribute to (1)J(P-31,P-31)(iso) indicates that the Fermi contact (FC) mechanism dominates in all cases where formal single P,P bonds exist and that the paramagnetic spin-orbit mechanism is of equal or greater importance in comparison with the FC mechanism in cases where formal multiple P,P bonds exist. Results from relativistic ZORA DFT calculations differ from the nonrelativistic calculations by less than 10%, indicating that inclusion of relativistic effects is not crucial, as anticipated, given that the systems investigated herein contain relatively light atoms (Z less than or equal to 24).