The bonding between phosphorus ligands X = PCl(3), PF(3), P(OCH(3))(3), PH(3), PH(2)CH(3), PH(CH(3))(2), P(CH(3))(3) and the metal-containing fragments [Ni(CO)(3)], [Mo(CO)(5)], and [Fe(CO)(4)] have been studied by Natural Orbitals for Chemical Valence (NOCV). The main attention was paid to estimation of donor (Deltaq(d)) /acceptor (Deltaq(bd)) properties of X on the basis of NOCV's charge criterion. All ligands X are found to be both sigma-donors and pi-acceptors. The best sigma-donor and pi-acceptor ligands are P(CH(3))(3) and PY(3) (Y horizontal line F,Cl), respectively, in both the nickel and molybdenum complexes. The NOCV contributions to deformation density show that the sigma-component corresponds to the donation from the lone electron pair of phosphorus, enhanced further by a transfer from ancillary halogen atoms (in the case of PCl(3) and PF(3)) to a bonding region and to oxygen atoms of carbonyls. The pi-bonding is due to the electron transfer from the metal into the empty orbital of X, mostly exhibiting phosphorus 3p character. It was shown that within the molecular orbital framework, the trend for the donor/acceptor strength of X can be explained by the difference in the orbital energies of the orbitals involved in the donation/back-donation. Regarding the influence of the metal fragment on the donor/acceptor properties of X, it was demonstrated that the relative order of the phosphorus ligands remains in general intact. The only exception is the P(OCH(3))(3) ligand changing its position in molybdenum series compared to the nickel complexes. However, a change in the metal-containing fragment can influence the magnitude of electron transfer. For the set of phosphorus ligands studied here the effect is much less pronounced than for other ligands studied previously.