TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Composition: An active material of positive electrode contains nickel and/or manganese atom. An active material of negative electrode contains carbon, silicon, titanium, or tin.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred composition: The electrolyte solution further contains aromatic compound, halogen-containing compound, polymeric compound, sulfur-containing compound, silicon-containing compound, nitrile compound, boron-containing compound or imide compound. The metal complex (b) is of formula (I), (II), Mn-NRm3Rm4 (III), or Mo-O (IV). The metal complex (II) is preferably of formula (IIa)-(IId). The phosphorus-containing compound is of formula: Ra11-P(=Xn)(-Ra12)(-Ra13) (a1) or -(P(-Ra21)(-Ra21)=N)n2- (a2). The phosphorus-containing compound (a2) is preferably of formula (a2-1) or (a2-2). The phosphorus-containing compound (a2-1) is preferably of formula (a2-1-1) or (a2-1-2). The concentration of component (a) and component (b) with respect to total quantity of electrolyte solution containing electrolyte is 0.5-30 %mass and 0.001-10 %mass, respectively. The content of the component (b) is 0.01-10 parts mass with respect to 100 parts mass component (a).Mm,Mn,Mo,=transition element or rare earth element;Rm1,Rm2=alkyl, alkylsilyl, alkenyl, alkynyl, alkoxy, thioalkoxy, amino, amido, acyloxy, cyano, carboxy, carbonyl-containing group, sulfanyl-containing group, phosphino, or halo;a,b=0-5;Xm,Ym=H, alkyl, alkenyl, alkoxy, alkylamino, silylamino, sulfonic acid group, isocyanato, isothiocyanato, sulfanil, phosphino, carbonyl-containing group, halo, aryl, or heteroaryl;m1,n1=integer;m1+n1=0-3;c=0-2;T1=group of formula (i), H, alkyl, alkenyl, alkoxy, alkylamino, silylamino, sulfonic acid group, isocyanato, isothiocyanato, sulfanil, phosphino, carbonyl-containing group, halo, aryl, or heteroaryl;Rm3,Rm4=H, alkyl, alkenyl, alkynyl, aryl, heteroaryl, alkylsilyl, or halo;M=center metal, more preferably Ti, Zr, Hf or V;A1=aryl or heteroaryl;R1=alkyl, aryl, heteroaryl or alkenyl;X=CR2 or N;R2,R7,R8=H, alkyl, alkenyl, hydroxy, alkoxy, aryloxy, thio, alkylthio, or arylthio;R1+R2=ring;R3,R4-R6=substituent;Y'=monodentate ligand;k=1-4;l=0-3;m=0-2;B1,B2=nitrogen-containing heteroaryl;L=alkylene, arylene, heteroarylene or alkenylene;n,o,p=0-3;Ra11-Ra13=alkyl, alkoxy, aryloxy, halo, amino or -(CH2)n3C(=O)-(O)m3Rb4;m3,n3=0 or 1;Rb4=alkyl, alkenyl, aryl or aralkyl;Xn=O, S or N (Ra14);Ra14=H or monovalent substituent;Ra21,Ra31-Ra36,Ra41-Ra48=monovalent substituent;andRa51-Ra52=alkoxy or dialkylamino, preferably dialkylamino.(i) Rm1 optionally forms aliphatic ring or aryl; (ii) Xm and Ym are mutually connected; (iii) Rm1 and Rm2 are mutually connected; (iv) Rm3 and Rm4 are mutually connected; and (iv) R4 and R6 is mutually bonded or condensed with portion of B1 and B2 to form ring.