Disclosed are substituted xanthines of general formula ##STR00001## wherein R.sup.1 to R.sup.4 are defined hereinbelow, the tautomers, the stereoisomers, the mixtures thereof, the prodrugs thereof and the salts thereof, which have valuable pharmacological properties, particularly an inhibitory effect on the activity of the enzyme dipeptidylpeptidase-IV (DPP-IV).