NOVELTY - A positive electrode active material contains hexagonal-type lithium-containing complex oxide particles (I) having layer structure and average particle diameter of 3-8 mu m. The ratio of difference of 90% average particle diameter and 10% average particle diameter in positive electrode active material with respect to average particle diameter of positive electrode active material is 0.6 or less.    USE - Positive electrode active material is used for nonaqueous electrolyte secondary battery (claimed). Uses include but are not limited to portable electronic device e.g. mobile telephone and notebook computer, power tool, electric vehicles, hybrid motor vehicles, combustion engine, gasoline engine and diesel engine.    ADVANTAGE - The positive electrode active material has uniform particle size distribution. The nonaqueous electrolyte secondary battery positive electrode active material has high durability, thermal stability, discharge capacity, output characteristics, and cyclic characteristics, and is safe.    DETAILED DESCRIPTION - A positive electrode active material contains hexagonal-type lithium-containing complex oxide particles of formula: Li1+sNixCoyMnzCatMguAvO2 (I) having layer structure and average particle diameter of 3-8 mu m. The ratio of difference of 90% average particle diameter and 10% average particle diameter in positive electrode active material with respect to average particle diameter of positive electrode active material is 0.6 or less.    s=0.05-0.2;    x+y+z+t+u+v=1;    x=0.3-0.7;    y,z=0.1-0.4;    t=0.0002-0.01;    u=0-0.005;    t+u+v=0.0002-0.02;and    A=sodium, aluminum, titanium, vanadium, chromium, zirconium, niobium, molybdenum, hafnium, tantalum and/or tungsten.    INDEPENDENT CLAIMS are included for the following:    (1) nonaqueous electrolyte secondary battery, which has positive electrode formed using positive electrode active material;    (2) nickel-cobalt-manganese composite hydroxide particles, which are of formula: NixCoyMnzCatMguAv(OH)2+a. The nickel-cobalt-manganese composite hydroxide particles contain secondary particles which are formed by aggregating several primary particles. The average particle diameter of secondary particles is 3-7 mu m. The ratio of difference of 90% average particle diameter and 10% average particle diameter in nickel-cobalt-manganese composite hydroxide particles with respect to average particle diameter of nickel-cobalt-manganese composite hydroxide particles is 0.55 or less;    (3) manufacture of nickel-cobalt-manganese composite hydroxide particles, which involves mixing aqueous solution containing nickel compound, cobalt compound, cobalt compound, manganese, calcium, and magnesium, adding ammonium-ion supply component, controlling pH to 12-14 at 25 degrees C, nucleating, forming aqueous solution containing nucleus, controlling the pH to less than the pH of nucleation process, growing nucleus, and washing with water; and    (4) manufacture of positive electrode active material, which involves heat-processing nickel-cobalt-manganese composite hydroxide particles at 105-400 degrees C, adding lithium compound, mixing at 800-1000 degrees C under oxidative atmosphere, baking and pulverizing.    a=0-0.5.