NOVELTY - The alkali metal air battery comprises a negative electrode (25) containing an active material, a positive electrode (23) containing oxygen as an active material, a non-aqueous ion-conducting medium configured to conduct alkali metal ions and arranged between the negative and positive electrodes, and a compound having a stable radical skeleton. The positive electrode and the non-aqueous ion-conducting medium contain the compound having the stable radical skeleton and serving as a redox catalyst (0.01-60 wt.%) for oxygen. The redox catalyst is a radical polymer.    USE - The alkali metal air battery is useful as a rechargeable secondary battery in electric cars.    ADVANTAGE - The alkali metal air battery exhibits improved charge and discharge potential, high capacity and improved efficiency using compound having the stable radical skeleton.    DETAILED DESCRIPTION - The alkali metal air battery comprises a negative electrode (25) containing an active material, a positive electrode (23) containing oxygen as an active material, a non-aqueous ion-conducting medium configured to conduct alkali metal ions and arranged between the negative and positive electrodes, and a compound having a stable radical skeleton. The positive electrode and the non-aqueous ion-conducting medium contain the compound having the stable radical skeleton and serving as a redox catalyst (0.01-60 wt.%) for oxygen. The redox catalyst is a radical polymer having the stable radical skeleton or a monomolecular compound having a structure in which the stable radical skeleton is linked to a polycyclic aromatic ring with a spacer such as an amide bond, an ester bond, a urea bond, a urethane bond, a carbamide bond, an ether bond or a sulfide bond. The redox catalyst is supported on a carbonaceous carrier having a cyclic structure in a monomolecular state by ultrasonic irradiation. The ion-conducting medium is a non-aqueous electrolytic solution containing the compound having the stable radical skeleton, where a hydrogen atom, aromatic rings or an amino group is bonded to the radical skeleton. The negative electrode occludes and discharges lithium ions. The ion-conducting medium conducts lithium ions.    DESCRIPTION OF DRAWING(S) - The diagram shows a cross-sectional view of an F-type electrochemical cell.    Positive electrode (23)    Gas reservoir (24)    Negative electrode (25)    Non-aqueous electrolytic solution (28)    Pressing member. (29)