Chiral phosphorus-containing ligands comprising at least one amine radical and at least one dihydrocarbylphosphinoxy radical of the formula W=OP (R).sub.2, in which R is a hydrocarbon radical selected from the group consisting of alkyl, aryl, and cycloalkyl radicals, wherein the ligand is selected from the group consisting of:those of the formula ##STR1## those of the formula ##STR2## those of the formula ##STR3## those of the formula ##STR4## in which formulae: R.sub.1 and R.sub.2 are selected from the group consisting of a hydrogen atom and hydrocarbon radicals;R.sub.3 and R.sub.4, which must be different from one another, are selected from the group consisting of a hydrogen atom and hydrocarbon radicals that may or may not carry at least one functional group selected from the group consisting of the alcohol, thiol, thioether, amine, imine, acid, ester, amide, and ether functional groups; andR.sub.5 and R.sub.6 are selected from the group consisting of hydrogen atoms and hydrocarbon radicals that may or may not contain functional groups.A process for their manufacture comprises reacting an optically active amino alcohol, in a hydrocarbon solvent at a temperature between -50.degree. and 80.degree. C. and under an inert gas atmosphere, with at least one compound of the formula P(R).sub.2 Y in which Y is chosen from among the halogen atoms and amine radicals, the compound being present in a molar ratio, relative to the amino alcohol, greater than or equal to the number of P(R).sub.2 groups to be introduced into the chiral molecule.The chiral phosphorous-containing ligands are used by reacting at least one organic compound that does not possess a center of asymmetry with (A), on the one hand, at least one transition metal complex of formula MZq in which M is a metal in group VIII of the Periodic Classification, q is the coordination number of the metal M, and Z is an atom or molecule capable of complexing the metal M and (B), on the other hand, at least one ligand L.