NOVELTY - A mixed aqueous solution (a) containing nickel salt and cobalt salt, and an aqueous solution (b) containing ammonium-ion supply component, are stirred, and a caustic-alkali aqueous solution (c) is added and reacted to obtain crystallized nickel-cobalt composite hydroxide particles. The obtained particles are separated into solid and liquid, washed with water and dried to obtain nickel-cobalt composite hydroxide (I). The ratio of the supply amount with respect to amount of reaction solution per supply port of mixed aqueous solution (a) is less than 0.04 volume% per minute.    USE - Manufacture of nickel-cobalt composite hydroxide used for positive electrode active material (both claimed) used for nonaqueous electrolyte secondary battery used as power supply for portable electronic device e.g. mobile telephone and notebook personal computer, hybrid vehicle and electric vehicle.    ADVANTAGE - The method efficiency provides nickel-cobalt composite hydroxide having high density and productivity. The nonaqueous electrolyte secondary battery using nickel-cobalt composite hydroxide has excellent charging/discharging stability and thermal stability.    DETAILED DESCRIPTION - A mixed aqueous solution (a) containing nickel salt and cobalt salt, and an aqueous solution (b) containing ammonium-ion supply component, are stirred using a stirring blade having inclination of 45 or less with respect to horizontal surface, and a caustic-alkali aqueous solution (c) is added and reacted to obtain crystallized nickel-cobalt composite hydroxide particles. The obtained particles are separated into solid and liquid, washed with water and dried to obtain nickel-cobalt composite hydroxide of formula: Ni1-x-yCoxMy(OH)2 (I). The ratio of the supply amount with respect to amount of reaction solution per supply port of mixed aqueous solution (a) is less than 0.04 volume% per minute.    C=0.05-0.95;    y=more than 0 to 0.15;    x+y=0.95 or less;and    M=additional element chosen from at least one of magnesium, aluminum, titanium, vanadium, chromium, manganese, zirconium, niobium, molybdenum and tungsten.    INDEPENDENT CLAIMS are included for the following:    (1) nickel-cobalt composite hydroxide, which is spherical-shaped particles having average particle diameter of 15-50 mu m; and    (2) positive electrode active material, which is obtained by mixing nickel-cobalt composite hydroxide and lithium compound, and baking.