The present invention relates to substituted xanthines of general formula ##STR00001## wherein R.sup.1 to R.sup.3 are defined as in claims 1 to 16, the tautomers, the stereoisomers, the mixtures, the prodrugs thereof and the salts thereof which have valuable pharmacological properties, particularly an inhibiting effect on the activity of the enzyme dipeptidylpeptidase-IV (DPP-IV).