Process for the synthesis of R(+)α-lipoic acid comprising the following stages: a) Salifying of racemic 6,8-halo-octanoic acid with S(-)α-methylbenzylamine; b) separation by filtration of the crystallized diastereoisomeric salt of R(+)6,8-di-halo-octanoic acid-S(-)α-methylbenzylamine; c) purification by re-crystallization of the diastereoisomeric salt of R(+)6,8-di-halo-octanoic acid-S(-)α-methylbenzylamine; d) separation of the diastereoisomeric salt to obtain R(+)6,8-di-halo-octanoic acid by reation of said salt with strong mineral acids in an aqueous solution with a dilution between 2 and 10% by weight; e) esterification of R(+)6,8-di-halo-octanoic acid to obtain the corresponding alkyl ester; f) reaction of the alkyl ester of R(+)6,8-di-halo-octanoic acid in an organic solvent with an aqueous solution of alkali disulfide in presence of a compound for phase transfer catalysis; g) hydolysis of the ester of R(+)α-lipoic acid.