The present invention concerns a new general process for asymmetric hemisynthesis of harringtonines and their analogs, that are alkaloids used in chemotherapy. This process comprises direct esterification of a natural cephalotaxine with an acylating compound constituted of a side chain precursor which backbone and functionalization are entirely preformed. The invention also concerns a natural, synthetic or semi-synthetic harringtonines including their tautomeric forms and their salts of the following formula: ##STR00001## wherein n=2 (i.e. harringtonine) or n=3 (i.e. homoharringtonine), in which the total content of impurities, possibly including enantiomeric forms, is lower than 1%, and/or the content of the major impurity is lower than 0.9%, and/or the chromatographic assay exhibits a harringtonines content higher than 97.5%.