Abstract: A 3-propenylcephem derivative of the following formula: ##STR1## wherein R.sub.1 represents a fluoro-substituted lower alkyl group or a cyano-substituted lower alkyl group, and A represents a cyclic or an acylic ammonio group, or a pharmaceutically acceptable salt thereof, exhibiting excellent anti-bacterial activities against both Gram-positive bacteria and Gram-negative bacteria; Process for the preparation thereof; Anti-bacterial composition; Intermediate for the 3-propenylcephem derivative; and Process for the preparation of the intermediate.