NOVELTY - A nonaqueous electrolyte contains an electrolytic salt dissolved in a nonaqueous solvent. The solvent contains two or more cyclic carbonate chosen from ethylene carbonate, propylene carbonate, 1,2-butylene carbonate, 2,3-butylene carbonate, 4-fluoro-1,3-dioxolan-2-one, trans or cis-4,5-difluoro-1,3-dioxolan-2-one, vinylene carbonate, vinyl ethylene carbonate, and 4-ethynyl-1,3-dioxolan-2-one. The electrolyte further contains 0.01-10 %mass cyclic acid anhydride (I) to which side chain containing at least three carbon atoms and having a double or triple bond at the end is bound.    USE - Nonaqueous electrolyte for electrical storage device (claimed). Uses include but are not limited to lithium secondary battery used as power supply for portable electronic device e.g. mobile telephone and notebook computer, electric vehicle, motor vehicle, hybrid electric vehicle, electric power storage, plug-in hybrid electric vehicle, battery electric vehicle, etc.    ADVANTAGE - The nonaqueous electrolyte has improved electrochemical properties over a wide temperature range and low-temperature discharge characteristics.    DETAILED DESCRIPTION - A nonaqueous electrolyte contains an electrolytic salt dissolved in a nonaqueous solvent. The nonaqueous solvent contains two or more cyclic carbonate chosen from ethylene carbonate, propylene carbonate, 1,2-butylene carbonate, 2,3-butylene carbonate, 4-fluoro-1,3-dioxolan-2-one, trans or cis-4,5-difluoro-1,3-dioxolan-2-one, vinylene carbonate, vinyl ethylene carbonate, and 4-ethynyl-1,3-dioxolan-2-one. The electrolyte further contains 0.01-10 %mass cyclic acid anhydride of formula (I) to which a side chain containing at least three carbon atoms and having a double or triple bond at the end is bound.    R1,R2=H, halo or 1-6C alkyl in which one or more H is optionally substituted by halo;and    R3=2-4C linear or branched alkenyl having double bond at terminal or 2-4C linear or branched alkynyl having triple bond at terminal.    An INDEPENDENT CLAIM is included for electrical storage device, which has the nonaqueous electrolyte, a positive electrode and a negative electrode.