NOVELTY - A cationic conductor comprises a block copolymer containing a polymer moiety (I) having specific structural unit, and a polymer moiety (II) having addition polymerizable monomers.    USE - For lithium secondary battery (claimed) used as power supply for portable electronic device, electric automobiles, electric bicycles, personal computers, cellular phones, digital cameras, camcorders, portable minidisk players, personal digital assistants, wrist watches, radio, electronic personal organizers, electric tools, vacuum cleaners, toys, elevators, robots for emergency purposes, walking-aid machines for healthcare purposes, wheelchairs for healthcare purposes, moving beds for healthcare purposes, emergency electric supplies, load conditioners, and electric power storage systems, and for power supply of military, space exploration and emergency purposes.    ADVANTAGE - The cationic conductor provides polymer electrolyte with excellent ionic conductivity. The leakage of battery formed using polymer electrolyte is prevented, and performance of battery is maintained at low temperature. The battery has high safety.    DETAILED DESCRIPTION - A cationic conductor comprises a block copolymer containing a polymer moiety (I) having specific structural unit, and a polymer moiety (II) having addition polymerizable monomers.    R=organic group obtained by polymerization of monomer compound having polymerizable unsaturated linkages;    Q=n+1 valence organic group bonded to R through a single bond;    Z=functional group capable of forming an ionic bond or having coordination ability to cation;    Mk+=k-valence cation;and    n,m=1 or more, such that Z forms ionic or coordination bond to cation.    An INDEPENDENT CLAIM is included for lithium secondary battery, which comprises an anode and a cathode wound or laminated via an interposing polymer electrolyte. The anode has an anode active material capable of intercalating and deintercalating lithium. The cathode has a cathode active material capable of intercalating and deintercalating lithium. The polymer electrolyte comprises the cationic conductor.    DESCRIPTION OF DRAWING(S) - The figure shows the lithium secondary battery.