The present invention relates to a process for preparing optically active hydroxy-, alkoxy-, amino-, alkyl-, aryl- or chlorine-substituted alcohols or hydroxy carboxylic acids having from 3 to 25 carbon atoms or their acid derivatives or cyclization products by hydrogenating the correspondingly substituted optically active mono- or dicarboxylic acids or their acid derivatives in the presence of a catalyst whose active component consists of rhenium or of rhenium and comprises at least one further element having an atomic number of from 22 to 83, with the provisos that a. the at least one further element having an atomic number of from 22 to 83 is not ruthenium and b. in the case of the preparation of optically active 2-amino-, 2-chloro-, 2-hydroxy- and 2-alkoxy-1-alkanols by catalytically hydrogenating corresponding optically active 2-aminocarboxylic acids, 2-chlorocarboxylic acids, 2-hydroxycarboxylic acids and 2-alkoxycarboxylic acids or their acid derivatives, the at least one further element having an atomic number of from 22 to 83 is not palladium or platinum.