Described herein is a cephem derivative represented by the general formula: ##STR1## wherein n stands for 1 or 2, Y stands for CH or nitrogen atom, R.sub.1 represents a lower hydrocarbon group or a carboxyl-substituted, a carbamoyl-substituted, or a cyclopropyl-substituted lower alkyl group, and R.sub.2 denotes hydroxyl group, a lower alkyl group, a hydroxy-substituted lower alkyl group, or carbamoyl group. The derivative is useful as an antibacterial composition. Also described herein are processes for the production of the derivative, antibacterial composition, intermediate of the derivative and process for the production thereof.