Semisynthetic diastereomerically pure N-glycidylanthracyclines, a process for the stereoselective preparation thereof and the use thereof as cytostatics. The invention relates to anthracyclines having cytostatic activity and the formula I, which are, where appropriate, in the form of a salt with an inorganic or organic acid, ##STR1## in which R.sup.1 is hydrogen or a hydroxyl group,R.sup.2 is hydrogen, a hydroxyl group or an alkyloxy group (C.sub.1 -C.sub.4),R.sup.3 is hydrogen, a hydroxyl group or a structure of the formula II ##STR2## R.sup.4 is CH.sub.2 CH.sub.3, COCH.sub.3, COCH.sub.2 OH, CHOHCH.sub.3 or CHOHCH.sub.2 OH,R.sup.5 is hydrogen, a hydroxyl group, a methoxycarbonyl group or a structure of the formula II,R.sup.6 is hydrogen, an alkyl group (C.sub.1 -C.sub.4), an allyl group, a benzyl group or mono- or di-methyloxy-substituted benzyl group, a tetrahydropyranyl group,R.sup.7 is hydrogen, an alkyl group (C.sub.1 -C.sub.4), an allyl group, a benzyl group or mono- or di-methyloxy-substituted benzyl group andR.sup.8 is a structure of the formula III or IV ##STR3## and to a process for the preparation of these compounds, which comprises reacting an anthracycline derivative of the structure I in whichR.sup.1, R.sup.2 and R.sup.4 are as defined above, andR.sup.3 is hydrogen, a hydroxyl group or a structure of the formula V ##STR4## R.sup.5 is hydrogen, a hydroxyl group, a methoxycarbonyl group or a structure of the formula V andR.sup.6 and R.sup.7 are as defined above, with (R)- or (S)-glycidyl sulfonate.