Abstract: 1. A ?-lactam compound of the formula [1]; wherein R1 is a lower alkyl, a lower alkyl substituted by a hydroxy; R2 is a hydrogen, a lower alkyl; X is O, S, NH; m and n are 0 to 4, Y1 is a halogen, cyano, a hydroxy, an amino, a lower alkyloxy, a lower alkylamino, a carboxy, a carbamoyl, a lower alkyl, etc., Y2 is hydrogen, an alkyl, cyano, —C(R3)?NR4 (wherein R3 and R4 are hydrogen, an amino, an alkyl, etc., or R3 and R4 may combine each other together with the nitrogen atom to form a 5- to 7-membered heterocyclic group), or a pharmaceutically acceptable salt thereof, or a non-toxic ester thereof, which has an excellent antibacterial activity against Gram-positive bacteria, especially against MRSA and MRCNS.