The present invention relates to substituted xanthines of the general formula ##STR00001## in which R.sup.1 to R.sup.3 and n are as defined in claims 1 to 8, their tautomers, their enantiomers, their diastereomers, their mixtures, their prodrugs and their salts, which have valuable pharmacological properties, in particular an inhibitory action on the activity of the enzyme dipeptidylpeptidase-IV (DPP-IV).