The present invention relates to bicyclic imidazole compounds of general formula ##STR00001## wherein R.sup.1 to R.sup.3 and A are defined as in claims 1 to 8, the tautomers, the enantiomers, the stereoisomers, the mixtures thereof and the salts thereof, which have valuable pharmacological properties, particularly an inhibiting effect on the activity of the enzyme dipeptidylpeptidase-IV (DPP-IV).