Substituted bicyclic beta-lactams of Formula I:are β-lactamase inhibitors, wherein a, X, R1 and R2 are defined herein. The compounds and pharmaceutically acceptable salts thereof are useful in the treatment of bacterial infections in combination with β-lactam antibiotics. In particular, the compounds can be employed with a β-lactam antibiotics (e.g., imipenem, piperacillin, or ceftazidime) against microorganisms resistant to β-lactam antibiotics due to the presence of the β-lactamases.