This invention provides Cephem compounds having the formula: or an ester, a protected compound at the amino on the ring in the 7-side chain, a pharmaceutically acceptable salt, or a solvate thereof, a pharmaceutical composition thereof, and a method for treating a bacterial infectious disease with the compound, the ester, the protected compound, the salt, or the solvate thereof, wherein the symbols in the formula are defined in the specification. The compounds exhibit potent antimicrobial spectrum against a variety of bacteria including Gram negative bacteria and/or Gram positive bacteria, preferably beta-lactamase producing Gram negative bacteria, more preferably, multi-drug resistant microbials, in particular, Class B type metallo-beta-lactamase producing Gram negative bacteria, and still preferably extended-spectrum beta-lactamase (ESBL) producing bacteria. The compounds most preferably do not exhibit cross-resistance against known Cephem drugs or Carbapenem drugs.