NOVELTY - An aqueous solution containing nickel salt and cobalt salt, and aqueous solution containing ammonium-ion supply component are mixed, and caustic-alkali aqueous solution is continuously supplied to obtain reaction solution. Nickel cobalt composite hydroxide particles are continuously crystallized by maintaining pH of reaction solution. The transition metal ion concentration in reaction solution is reduced, and reaction solution is separated. Nickel cobalt composite hydroxide particles are washed, and dried to obtain nickel cobalt composite hydroxide (I).    USE - Manufacture of nickel cobalt composite hydroxide used as precursor of positive electrode active material of nonaqueous electrolyte secondary battery used as power supply for mobile telephone, notebook personal computer, electric vehicles and hybrid motor vehicles.    ADVANTAGE - The method efficiently provides high yield of nickel cobalt composite hydroxide with target particle size distribution, and specific surface area. The outflow of transition metal is suppressed by adjusting the pH of the reaction solution, during manufacture of nickel cobalt composite hydroxide.    DETAILED DESCRIPTION - An aqueous solution containing nickel salt and cobalt salt, and aqueous solution containing ammonium-ion supply component are mixed, and caustic-alkali aqueous solution is continuously supplied to obtain a reaction solution. Nickel cobalt composite hydroxide particles are continuously crystallized by maintaining the pH of the reaction solution in specified range. Caustic-alkali aqueous solution is continuously supplied to the reaction solution containing nickel cobalt composite hydroxide particles continuously discharged during crystallization process, and the pH of the reaction solution is increased to 12.5 or more at 25 degrees C. The transition metal ion concentration in reaction solution is reduced, and the reaction solution containing pH-controlled nickel cobalt composite hydroxide particles is separated into solid and liquid. Nickel cobalt composite hydroxide particles are washed with water, and dried to obtain nickel cobalt composite hydroxide of formula: Ni1-x-y-zCoxMnyMz(OH)2 (I).    x=more than 0 and less than 1/2;    y=0 to less than 1/2;    z=0-0.1;and    M=Mg, Al, Ca, Ti, V, Cr, Zr, Nb, Mo or W.