NOVELTY - A reaction aqueous solution (HH) containing a mixed aqueous solution (GG) containing a metallic compound and an aqueous ammonia solution is stirred. The nickel ion concentration of reaction aqueous solution is maintained at 0.1-5 mass ppm, to form (AA,II) seed particles. The formed seed particles are grown (BB,MM) by stirring an aqueous solution (B) obtained by feeding mixed aqueous solution and aqueous ammonium solution (DD) to the seed particles-containing reaction aqueous solution, to form particles (NN) containing nickel-cobalt composite hydroxide (I).    USE - Manufacture of nickel-cobalt composite hydroxide used for positive electrode active material for nonaqueous electrolyte secondary battery for mobile telephone, notebook personal computer, hybrid vehicle and electric vehicle.    ADVANTAGE - The method enables manufacture of nickel-cobalt composite hydroxide having uniform particle size and reduced particle size distribution, with high productivity by a simple process. The nonaqueous electrolyte secondary battery containing the positive electrode active material has excellent cycle characteristics.    DETAILED DESCRIPTION - A reaction aqueous solution containing a mixed aqueous solution containing a metallic compound chosen from aluminum, magnesium, titanium, iron, copper, zinc and gallium and an aqueous ammonia solution containing an ammonium ion donor is stirred with the impeller discharge head (H1) adjusted to 50-100 m2/second2. The nickel ion concentration of the reaction aqueous solution is maintained at 0.1-5 mass ppm, to form seed particles. The formed seed particles are grown by stirring an aqueous solution (B) having nickel ion concentration of 5-300 mass ppm and obtained by feeding a mixed aqueous solution and an aqueous ammonium solution to the reaction aqueous solution containing the seed particles. The nickel ion concentration of obtained solution is maintained more than the nickel ion concentration during formation of the seed particles, to form particles containing nickel-cobalt composite hydroxide of formula: Ni1-x-yCoxMnyMz(OH)2 (I).    x=0.05-0.95;    y=0-0.55;    z=0-0.1;    x+y+z=less than 1;and    M=aluminum, magnesium, titanium, iron, copper, zinc and gallium.    An INDEPENDENT CLAIM is included for nickel cobalt composite hydroxide, which has ratio of difference of particle size (D50) and particle size (D10) to particle size (D50) of 0.25 preferred less measured based on laser beam diffraction scattering-type particle size analysis, and ratio of difference of particle size (D90) and particle size (D50) to particle size (D10) of 0.25 or less measured based on laser beam diffraction scattering-type particle size analysis, when volume integration value 10% is set to D(10), volume integration value 50% is set to D50 and volume integration value 90% is set to D(90).    DESCRIPTION OF DRAWING(S) - The drawing shows a flowchart explaining manufacture of nickel-cobalt composite hydroxide. (Drawing includes non-English language text)    Seed particles formation process (AA,II)    Seed particles growth process (BB,MM)    Mixed aqueous solution and aqueous ammonium solution (DD)    Mixed aqueous solution (GG)    Reaction aqueous solution (HH)    Particles containing nickel-cobalt composite hydroxide (NN)