A class of 7-oxo-2,6-diazabicyclo-[3.2.0]-heptane-6-sulfonic acid compounds substituted at the two position of the bicyclic ring with a heterocyclylaminocarbonyl group or a carbocyclylaminocarbonyl group are β-lactamase inhibitors. The compounds and their prodrugs and pharmaceutically acceptable salts are useful in the treatment of bacterial infections in combination with β-lactam antibiotics. In particular, the compounds are suitable for use with β-lactam antibiotics (e.g., imipenem and ceftazidime) against micro-organisms resistant to β-lactam antibiotics due to the presence of the β-lactamases.