NOVELTY - A non-aqueous electrolyte contains substituted phosphorus compound (I).    USE - Non-aqueous electrolyte for a lithium secondary battery that is utilized in a portable apparatus such as notebook personal computer, mobile personal computer, mobile telephone, headphone stereocassette tape recorder, video movie, liquid crystal TV, handy cleaner, electronic organizer, calculator, radio, backup power supply use, lighting fixture, game machine, timepiece, electric tool and camera, and in a motor, a motor vehicle, an electric vehicle, a motorbike, an electric motorcycle, a bicycle, and an electric-power-assisted bicycle.    ADVANTAGE - The electrolyte has high output characteristics, charging and discharging capacity, durability and energy density.    DETAILED DESCRIPTION - A non-aqueous electrolyte contains substituted phosphorus compound of formula ((R1)(R2)(R3)P(=O)n) (I).    R1=(-O-C(R4)(R5)-C(R6)(R7)-Si(R8)(R9)(R10));    R4-R7=H, 1-12C alkyl or phenyl;    R8-R10=1-12C alkyl, 2-12C alkenyl, 1-12C alkoxy or phenyl;    R2=phenyl or phenoxy (both optionally substituted by halo), H, 1-12C alkyl, 1-12C haloalkyl, 2-12C alkenyl, 1-12C alkoxy, 1-12C haloalkoxy or 2-12C alkenyloxy;    R3=phenyl, phenoxy or 5 or 6 membered heterocyclic group (all optionally substituted by halo), 1-12C alkyl, 1-12C haloalkyl, 2-12C alkenyl, 1-12C alkoxy, 1-12C haloalkoxy, 2-12C alkenyloxy, -Ra1-C(=O)-R11, -Ra1-P(=O)(R13)(R12), or -Ra1-S(=O)2-R14;    R2+R3,R12+R13=-O-CH2-(CH2)m-O-;    m=1-3;    Ra1=halo-substituted 1-6C bivalent hydrocarbon;    R11-R14=phenyl or phenoxy (both optionally substituted by halo), H, 1-12C alkyl, 1-12C haloalkyl, 2-12C alkenyl, 1-12C alkoxy, 1-12C haloalkoxy or 2-12C alkenyloxy.    INDEPENDENT CLAIMS are also included for the following:    (1) an additive for a lithium secondary battery, comprising substituted phosphorus compound (I) as an active ingredient    (2) substituted phosphorus compound (I)    (3) a lithium secondary battery comprising a positive electrode, metal or alloy with metallic lithium, a lithium containing alloy, and a negative electrode containing oxide, transition-metal nitride, and carbon material.    DESCRIPTION OF DRAWING(S) - The drawing shows a sectional view of a lithium secondary battery.    Positive electrode (1)    Negative electrode (2)    Positive electrode can (3)    Sealing board (4)    Separator (5)    Gasket (6)    Spacer board (7, 8)