NOVELTY - An aqueous solution containing an ammonium ion supplying material and a metal compound containing nickel, cobalt and manganese, is subjected to nucleation process, and the pH of aqueous solution is adjusted to 12-14 at liquid temperature of 25 degrees C. The resultant aqueous solution containing nuclei, is subjected to particle growth step, and pH of the aqueous solution is adjusted to 10.5-12 at liquid temperature of 25 degrees C to obtain nickel-cobalt-manganese composite hydroxide particles (I).    USE - Manufacture of nickel-cobalt-manganese composite hydroxide particles used for manufacture of positive electrode active material for nonaqueous electrolyte secondary battery (both claimed) used as power supply for notebook personal computer, mobile telephone, electric vehicles and hybrid vehicles.    ADVANTAGE - The nonaqueous electrolyte secondary battery using nickel-cobalt-manganese composite hydroxide particles has high capacity, thermal stability, durability, output characteristics and charging/discharging characteristics, and is safe and lightweight.    DETAILED DESCRIPTION - An aqueous solution containing an ammonium ion supplying material and a metal compound containing nickel, cobalt and manganese, is subjected to nucleation process, and the pH of the aqueous solution is adjusted to 12-14 at liquid temperature of 25 degrees C. The resultant aqueous solution containing nuclei, is subjected to particle growth step, and pH of the aqueous solution is adjusted to 10.5-12 at liquid temperature of 25 degrees C to obtain nickel-cobalt-manganese composite hydroxide particles of formula: NixCoyMnzMt(OH)2+(~a) (I).    X=0.3-0.7;    y=0.1-0.4;    z=0.1-0.5;    t=0-0.02;    x+y+z+t=1;    alpha =0-0.5;and    M=titanium, vanadium, chromium, aluminum, magnesium, zirconium, niobium, molybdenum hafnium, tantalum and tungsten.    INDEPENDENT CLAIMS are included for the following:    (1) nickel-cobalt-manganese composite hydroxide particles, which are obtained by aggregating spherical secondary particles and plate-shaped primary particles having average thickness of 10-300 nm and average length of 100-3000 nm in a random direction;    (2) manufacture of positive electrode active material. Nickel-cobalt composite hydroxide particles are heated, and lithium compound is added. The resultant mixture is baked at 800-1000 degrees C to obtain composite electrode active material containing lithium-nickel-cobalt-manganese complex oxide of formula: Li1+uNixCoyMnzMtO2 (II) having hexagonal-type lithium-containing complex oxide having layer structure. The ratio of number of atoms other than lithium with respect to number of lithium atoms is 1:0.95-1.2; and    (3) nonaqueous electrolyte secondary battery, which has a positive electrode and positive electrode active material.    u=-0.05 to 0.2.