The cleavage of the ribonucleotide UpU by imidazole buffers shows kinetic behavior that indicates a sequential bifunctional mechanism, in which the imidazolium ion acts first. Similar results are obtained for the cleavage of ApA. This mechanism is related to the simultaneous bifunctional cleavage of RNA by the enzyme ribonuclease, and has guided us to the synthesis of an improved cyclodextrin-bis-imidazole enzyme mimic that also uses a simultaneous bifunctional mechanism.