NOVELTY - A nickel cobalt composite hydroxide has specific surface area of 1-10 m2/g measured by nitrogen adsorption BET method, and carbon content of 0.1 %mass or less measured by a high frequency-infrared combustion method. The nickel cobalt composite hydroxide is used as precursor of positive electrode active material of a nonaqueous electrolyte secondary battery.    USE - Nickel cobalt composite hydroxide is used as precursor of positive electrode active material of nonaqueous electrolyte secondary battery e.g. lithium-ion secondary battery, for mobile telephone, motor vehicle and notebook-type personal computer.    ADVANTAGE - The light weight nickel cobalt composite hydroxide has high density with controllable surface property. The nonaqueous electrolyte secondary battery using the precursor of positive electrode active material using the nickel cobalt composite hydroxide has excellent thermal stability and battery characteristics.    DETAILED DESCRIPTION - A nickel cobalt composite hydroxide is of formula: Ni1-x-y-zCoxMnyMz(OH)2 (I), and has specific surface area of 1-10 m2/g measured by nitrogen adsorption BET method, and carbon content of 0.1 %mass or less measured by a high frequency-infrared combustion method. The nickel cobalt composite hydroxide is used as precursor of positive electrode active material of a nonaqueous electrolyte secondary battery.    x=more than 0 and 1/3 or less;    y=more than 0 and 1/3 or less;    z=0-0.1;and    M=magnesium, aluminum, calcium, titanium, vanadium, chromium, zirconium, niobium, molybdenum or tungsten.    An INDEPENDENT CLAIM is included for manufacture of nickel cobalt composite hydroxide (I), which involves mixing a mixed aqueous solution containing nickel salt and/or cobalt salt, and an aqueous solution containing an ammonium-ion supply material, supplying caustic-alkali aqueous solution, maintaining pH of the reaction solution of 11-13 at 25 degrees C based on liquid temperature standard, crystallizing nickel cobalt composite hydroxide particle in the reaction solution, separating into solid and liquid, washing the crystallized nickel cobalt composite hydroxide particles with water, drying the obtained nickel cobalt composite hydroxide particles at 100-230 degrees C which is maximum temperature of material temperature. When the drying temperature is T (in degrees C), the drying process is carried out until drying temperature reaches to less than (500/T).