NOVELTY - A nonaqueous electrolyte solution contains an electrolyte and a nonaqueous solvent. The electrolyte solution contains compound (A), and monofluorophosphate and/or difluorophosphate. Compound (A) is phosphoric acid compound, phosphorous acid compound, boric acid compound, or dicarboxylic acid in which hydrogen atom(s) is substituted by metal-containing group (a), dicarboxylic acid, and/or sulfated compound in which hydrogen atom(s) of sulfuric acid is substituted by metal-containing group (a).    USE - Nonaqueous electrolyte solution is used for secondary batteries (claimed) e.g. lithium secondary batteries used for electronic devices. Uses include but are not limited to notebook personal computers, electronic book players, mobile telephones, portable printers, liquid-crystal televisions, transceivers, motors, motor vehicles, toys, game machine devices, electric tools, and cameras.    ADVANTAGE - The nonaqueous electrolyte solution provides secondary batteries having excellent low-temperature discharge characteristics, large-current discharge characteristics, high-temperature storage characteristics, and cycle characteristics.    DETAILED DESCRIPTION - A nonaqueous electrolyte solution contains an electrolyte and a nonaqueous solvent. The electrolyte solution contains compound (A), and monofluorophosphate and/or difluorophosphate. Compound (A) is phosphoric acid compound in which hydrogen atom(s) is substituted by metal-containing group (a), phosphorous acid compound in which hydrogen atom(s) is substituted by metal-containing group (a), boric acid compound in which hydrogen atom(s) is substituted by metal-containing group (a), sulfated compound in which hydrogen atom(s) of sulfuric acid is substituted by metal-containing group (a), and dicarboxylic acid and/or dicarboxylic acid compound in which hydrogen atom(s) is substituted by metal-containing group (a). Group (a) is of formula: -M(-R1)(-R3)-R2.    M=Si, Ge, Sn or C;and    R1-R3=H, halo, or 1-10C hydrocarbyl optionally substituted by halo.    An INDEPENDENT CLAIM is included for secondary battery provided with a negative electrode and a positive electrode which occlude and discharge metal ions, and the nonaqueous electrolyte solution.