The present invention relates to substituted imidazo-pyridinones and imidazo-pyridazinones of general formula ##STR00001## wherein R.sup.1 to R.sup.4 are defined as in claim 1, the tautomers, the stereoisomers, the mixtures thereof and the salts thereof, which have valuable pharmacological properties, particularly an inhibitory effect on the activity of the enzyme dipeptidylpeptidase-IV (DPP-IV).