A nonaqueous secondary battery comprising: a positive electrode having a positive electrode mixture layer, a negative electrode, and a nonaqueous electrolyte, wherein the positive electrode comprises, as active materials, at least two lithium-containing transition metal oxides having different average particle sizes, and the lithium-containing transition metal oxide having the smallest average particle size is a lithium-containing transition metal oxide represented by the formula (1):
Li_xM¹_yM²_zM³_vO₂ (1) wherein M¹represents at least one transition metal element selected from Co, Ni and Mn, M²represents Mg and at least one metal element selected from the group consisting of Ti, Zr, Ge, Nb, Al and Sn, M³represents at least one element selected from the group consisting of Na, K, Rb, Be, Ca, Sr, Ba, Sc, Y, La, Hf, V, Ta, Cr, Mo, W, Tc, Re, Fe, Ru, Rh, Cu, Ag, Au, B, Ca, In, Si, P and Bi, and x, y, z and v are numbers satisfying the equations respectively: 0.97≦x<1.02, 0.8≦y<1.02, 0.002≦z≦0.05, and 0≦v≦0.05, and has an average particle size from 2 μm to 10 μm, and the lithium-containing transition metal oxide having the largest average particle size is a lithium-containing transition metal oxide represented by the formula (2):
Li_aM¹_bM²_cM³_dO₂ (2) wherein M¹, M²and M³are the same as defined in the formula (1), and a, b, c and d are numbers satisfying the equations respectively: 0.97≦a<1.02, 0.8≦b<1.02, 0.0002≦c≦0.02, and 0≦d≦0.02, and has an average particle size from 5 μm to 25 μm, wherein said electrolyte contains a fluorine-containing organic solvent, wherein the content of Co in the transition metal M¹of the formulae (1) and (2) is from 30% by mole to 100% by mole, wherein the content of said lithium-containing transition metal oxide having the smallest average particle size in the lithium-containing transition metal oxides is from 5% by weight to 60% by weight, wherein the content of said lithium-containing transition metal oxide having the largest average particle size in the lithium-containing transition metal oxides is from 40% by weight to 95% by weight, and wherein an amount of said fluorine-containing organic solvent is 0.1% by weight to 30% by weight based on the whole weight of the electrolyte. view more

The nonaqueous secondary battery according to claim 1, wherein the lithium-containing transition metal oxide having the largest average particle size is a lithium-containing transition metal oxide represented by the formula (wherein c and d satisfy the following equation, respectively: 0.0002≦c<0.005 and 0≦d<0.005. view more

The nonaqueous secondary battery according to claim 2, wherein z in the formula (1) is larger than c in the formula (2).

The nonaqueous secondary battery according to claim 1, wherein z in the formula (1) is larger than c in the formula (2).

The nonaqueous secondary battery according to claim 1, wherein, in the formula (1), the metal elements M&lt;sup&gt;2&lt;/sup&gt;are Mg and at least one metal element selected from the group consisting of Ti, Zr, Ge, Nb, Al and Sn; a content of Mg is from 0.1% by s than 2% by mole based on the amount of the transition metal M¹; when Ti, Zr, Ge or Nb is contained, a total content thereof is from 0.0by mole to less than 0.by mole based on the amount of the transition metal M¹; and when Al or Sn is contained, a total content thereof is from 0.1% by mole to less than 1% by mole based on the amount of the transition metal M¹. view more

The nonaqueous secondary battery according to claim 1, wherein, in the formula (2), the metal elements M&lt;sup&gt;2&lt;/sup&gt;are Mg and at least one metal element selected from the group consisting of Ti, Zr, Ge, Nb, Al and Sn; a content of Mg is from 0.01% less than 0.5% by mole based on the amount of the transition metal M¹; when Ti, Zr, Ge or Nb is contained, a total content thereof is from 0.005% by mole to less than 0.3% by mole based on the amount of the transition metal M¹; and when Al or Sn is contained, a total content thereof is from 0.01% by mole to less than 0.5% by mole based on the amount of the transition metal M¹. view more

The nonaqueous secondary battery according to claim 1, wherein said positive electrode mixture layer has a density of 3.5 to 4.6 g/cm&lt;sup&gt;3&lt;/sup&gt;.

The nonaqueous secondary battery according to claim 1, wherein said electrolyte further contains a fluorine-containing aromatic compound other than said fluorine-containing organic solvent.

The nonaqueous secondary battery according to claim 1, wherein the fluorine-containing organic solvent is fluoroethylene carbonate.

The nonaqueous secondary battery according to claim 1, wherein M&lt;sup&gt;1&lt;/sup&gt;represents Co.

A method of using a nonaqueous secondary battery according to claim 1 comprising the step of: charging the battery so that a positive electrode voltage is in a range of 4.35 to 4.6 V with reference to the potential of lithium when the battery is fully charged. view more