NOVELTY - An aqueous solution containing metallic compound (CC) is crystallized, ammonium-ion supply component is controlled, and pH is adjusted. The resulting mixture is nucleated under oxidative atmosphere having oxygen concentration of 1 vol.% or more, aqueous solution containing nucleus is formed and allowed to grow. The growth of particles is carried out in mixing atmosphere of oxygen and inert gas. The metallic compound is subjected to particle-growth process, and aluminum compound is coated to nickel-cobalt composite hydroxide, to obtain nickel composite hydroxide (I).    USE - Manufacture of nickel composite hydroxide used for active material of positive electrode of nonaqueous electrolyte secondary battery (all claimed) e.g. lithium-ion secondary battery. Uses include but are not limited to portable electronic device, mobile telephone, notebook-type personal computer, electric vehicle, and hybrid motor vehicle.    ADVANTAGE - The nonaqueous electrolyte battery containing the nickel composite hydroxide has excellent cycle characteristics, high capacity, reduced size, safety and excellent battery characteristics.    DETAILED DESCRIPTION - An aqueous solution containing metallic compound of formula: NixCoyAlxMntMs (a) is subjected to crystallization reaction, ammonium-ion supply component is controlled, and pH is adjusted to 12-14 at standard liquid temperature of 25 degrees C. The resulting mixture is nucleated under oxidative atmosphere having oxygen concentration of 1 vol.% or more, the aqueous solution containing the nucleus is formed in the nucleation process, pH is controlled to 10.5-12 at standard liquid temperature of 25 degrees C, and nucleus is allowed to grow. The growth of particles is carried out in 1-15% of time from start time of particle-growth process with respect to whole time from the start of particle growth process, and the condition is switched from oxidative atmosphere to mixing atmosphere of oxygen having oxygen concentration of 1 vol.% or less, and inert gas. The metallic compound of formula: Nix1Coy1Alz1Mnt1Ms1 (b) is subjected to particle growth process, and aluminum compound is coated to nickel-cobalt composite hydroxide obtained at particle-growth process, when aluminum is not contained in metallic compound supplied in the metallic compound contained in aqueous solution, to obtain nickel composite hydroxide of formula: Nix3Coy3Alz3Mnt3Ms3(OH)2+a (I).    x3+y3+z3+t3+s3=1;    y1,y3=0-0.3;    z1,z3=0-0.1 (excluding 0);    t3=0.001-0.05;    s1,s3=0-0.05;    a=0-0.5;    M=Mg, Ca, Ti, V, Cr, Zr, Nb, Mo and W;    x+y+z+t+s=1;    y=0-0.8;    z=0-0.1;    t=0.1-0.8;    s=0-0.05;    x1+y1+z1+t1+s1=1;and    t1=0-0.05 (excluding 0.05).    INDEPENDENT CLAIMS are included for the following:    (1) nickel composite hydroxide, which consists of ultrafine primary particles having an average-particle diameter of 0.01-0.3 mu m present on central portion, and larger plate-shaped primary particles having average-particle diameter of 0.3-3 mu m, which is larger than ultrafine primary particles, present on shell. The thickness of outer shell portion is 5-45% with respect to particle diameter of secondary particles;    (2) manufacture of positive electrode active material, which spherical-shaped secondary particles, and lithium-nickel complex oxide of formula: Li1+uNixCoyAlzMntMsO2 (II) having hexagonal crystal structure, heat-processing nickel-cobalt-aluminum composite hydroxide at 105-750 degrees C, mixing lithium compound, forming lithium mixture, and baking lithium mixture at 700-800 degrees C in oxidative atmosphere.; and    (3) nonaqueous electrolyte secondary battery.    u=-0.05-0.2;    x+y+z+t+s=1;    y=0-0.3;    z=0-0.1 (excluding 0);    t=0.001-0.05;and    s=0-0.05.    DESCRIPTION OF DRAWING(S) - The drawing shows a flowchart explaining the process of manufacturing nickel composite hydroxide. (Drawing includes non-English language text)    Water (AA)    Aqueous alkali solution and aqueous ammonium solution (BB)    Metallic compound (CC)    Aqueous mixture (EE)    Nucleation (GG)