NOVELTY - Manufacture of nickel composite hydroxide particles involves nucleating aqueous solution containing metallic compounds by adjusting pH of aqueous solution to 11.5-13.2 based on liquid temperature of 25 degrees C, forming nucleus containing primary particles (a), and growing particles on the obtained nucleus by controlling pH of aqueous solution containing nucleus to 9.5-11 based on liquid temperature of 25 degrees C. The outer shell portion formed on the nucleus contains plate-shaped primary particles which is larger than the primary particles (a).    USE - Manufacture of nickel composite hydroxide particles used for manufacturing active material for positive electrode of nonaqueous electrolyte secondary battery (all claimed). Uses include but are not limited to mobile telephone, hybrid motor vehicle, electric hybrid, notebook-type personal computer, gasoline engine and diesel engine.    ADVANTAGE - The nickel composite hydroxide particles are manufactured efficiently with excellent solubility, and provide positive-electrode active material with excellent electrical resistance. The nonaqueous electrolyte secondary battery including active material has excellent battery characteristics, durability, thermal stability and high capacity. The initial discharge capacity of battery is 170 mAH/g or more.    DETAILED DESCRIPTION - Manufacture of nickel composite hydroxide particles involves nucleating aqueous solution containing metallic compounds by adjusting pH of aqueous solution to 11.5-13.2 based on liquid temperature of 25 degrees C, forming nucleus containing primary particles (a), and growing particles on the obtained nucleus by controlling pH of aqueous solution containing nucleus to 9.5-11 based on liquid temperature of 25 degrees C. The outer shell portion formed on the nucleus contains plate-shaped primary particles which is larger than the primary particles (a). The metallic compound has metal atomic ratio corresponding to metal atomic ratio in the particles of the nickel complex oxide, and does not contain complex-ion formation agent. The nickel composite hydroxide particles are of compositional formula: Ni1-x-yCoxMy(OH)2+a (I).    x=0-0.22;    y=0-0.15;    x+y=less than 0.3;    a=0-0.5;and    M=Mg, Al, Ca, Ti, V, Cr, Mn, Zr, Nb, Mo or W.    INDEPENDENT CLAIMS are included for the following:    (1) nickel composite hydroxide particles;    (2) manufacture of positive electrode active material;    (3) positive electrode active material; and    (4) nonaqueous electrolyte secondary battery.