This invention provides a quinolone derivative having potent antibacterial activity against various bacteria including drug-resistant strains which is a compound of the following formula wherein R1 is an optionally substituted aromatic group, a salt of the same or a hydrate of both. In the formula, R2, R3: hydrogen atom, an alkyl group; R4, R5, R6: hydrogen atoms, hydroxyl group, a halogen atom, carbamoyl group, an alkyl group, an alkoxyl group, an alkylthio group; R7, R8: hydrogen atom, an alkyl group; R9: an alkyl group, an alkenyl group, a halogenoalkyl group, a cyclic alkyl group, an aryl group, a heteroaryl group, an alkoxyl group having from 1 to 6 carbon atoms, an alkylamino group; R10: hydrogen atom, an alkylthio group; R11: hydrogen atom, amino group, hydroxyl group, thiol group, a halogenomethyl group, an alkyl group, an alkenyl group, an alkynyl group, an alkoxyl group; X1: halogen atom, a hydrogen atom; A1: nitrogen atom, C—X2; X2: hydrogen atom, amino group, a halogen atom, cyano group, an halogenomethyl group, a halogenomethoxyl group, an alkyl group, an alkenyl group, an alkynyl group, an alkoxyl group; A2, A3: >C═C(—A1═)—N(—R9)—, >N—C(—A1═)═C(—R9)—; R10 and R9 or R9 and X2 may be integrated to form a ring structure; and Y: hydrogen atom, ester forming group.