NOVELTY - A solid polymer electrolyte comprises a polymer compound having a branched carbonate structure, and electrolyte salt(s).    USE - For use in battery, in electric double-layer capacitor, and in electrochromic device.    ADVANTAGE - The inventive solid polymer electrolyte exhibits high ionic conductivity, and excellent processability, durability, safety and reliability. It is free of liquid leakage and has low production cost. It provides primary and secondary batteries that are capable of working with high capacity and current; electric double-layer capacitor that ensures high output voltage, large take-out current and good processability; and electrochromic device having high response speed.    DETAILED DESCRIPTION - A solid polymer electrolyte comprises a polymer compound having a branched carbonate structure of formula (I) or (II) as a partial structure, and electrolyte salt(s).    -(-(CR1R2)m-O-C(O)-)n- (I)    -(-(CHR3)m-O-C(O)-)n- (II)    R1, R2, R3 = H, 1-10C alkyl, 1-10C alkoxy, or 1-10C alkoxyalkyl;    m = 3-10;    n = 1-500.    R1, R2, and R3 are not hydrogen at the same time.    INDEPENDENT CLAIMS are also included for (A) a polymerizable composition for the solid polymer electrolyte comprising a polymerizable compound(s) of formula H2C=C(-R4)-C-C(O)- (III), H2C=C(R4)-C(O)-(OR5)x-N(R6)-C(O)-O- (IV),    H2C=C(R4)-C(O)-(OR5)x-N(R6)-C(O)-O- (V), or    H2C=C(R4)-C(O)-(OR5)x-N(R6)-C(O)-O-((CR1R2)m-O-C(O)-O-)-R7n- (VI)    and electrolyte salt(s);    R4 = 1-10C alkyl;    R5 = divalent group that may contain a heteroatom;    R6 = H, 1-10C alkyl, 1-10C alkoxy, or 1-10C alkoxyalkyl;    R7 = 1-30C organic group that may contain a heteroatom and/or an unsaturated bond;    x = 0 or 1    (B) a battery comprising the solid polymer electrolyte (7), a positive electrode (2), and a negative electrode (4);    (C) an electric double-layer capacitor comprising the solid polymer electrolyte and a pair of polarizable electrodes; and    (D) an electrochromic device comprising the solid polymer electrolyte and an electrochromic layer.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic cross-sectional view of the thin battery.    Positive electrode (2)    Negative electrode (4)    Solid polymer electrolyte (7)