NOVELTY - Manufacture of manganese-nickel-titanium composite hydroxide particles involves mixing aqueous solution which does not contain titanium, aqueous alkali solution, and aqueous solution containing manganese, nickel and ammonium-ion supply component, controlling pH value, nucleating the obtained product in an oxidative atmosphere, and carrying out particle growth process which controls pH of the aqueous solution during nucleation process and switching the aqueous solution which does not contain titanium to the aqueous solution which contains manganese, nickel, and titanium.    USE - Manufacture of manganese-nickel-titanium composite hydroxide particles used for manufacture of positive electrode material (all claimed). Uses include but are not limited to mobile telephone, notebook computer, and power supply for electric vehicle, hybrid vehicle, gasoline engine and diesel engine.    ADVANTAGE - The method enables economical and easy manufacture of manganese-nickel-titanium composite hydroxide particles, and provides positive electrode material having excellent output characteristics.    DETAILED DESCRIPTION - Manufacture of manganese-nickel-titanium composite hydroxide particles involves mixing aqueous solution which does not contain titanium, aqueous alkali solution, and aqueous solution containing manganese, nickel and ammonium-ion supply component, controlling pH value to 12-14 at 25 degrees C of liquid temperature standard, carrying out nucleation process of nucleating the obtained product by an oxidative atmosphere, and carrying out particle growth process which controls pH of the aqueous solution during nucleation process to 10.5-12 at 25 degrees C of liquid temperature standard, and makes the nucleus to grow, and in which, While oxygen concentration switches the oxidative atmosphere to weakly oxidizable atmosphere or a nonoxidizing atmosphere of 1-30 vol.% with respect to whole particle growth process time from the start time of the particle growth process, and switching the aqueous solution which does not contain titanium to the aqueous solution which contains manganese, nickel, and titanium. The manganese-nickel-titanium composite hydroxide particles comprises Mn1-xy- zNixTiyMz(OH)2+(~a).    x=0.20-0.28;    y=0-0.05;    z=0-0.05;    ( alpha )=0-0.5;and    M=elements chosen from Mg, Ca, Ba, Sr, V, Fe, Cr, Co, Cu, Zr, Nb, Mo, and W.    INDEPENDENT CLAIMS are included for the following:    (1) manganese-nickel-titanium composite hydroxide particles, which comprises primary particles formed by aggregating spherical shaped secondary particles, center portion containing fine primary particles and outer shell portion which becomes outer side of center portion from bigger primary particle than fine primary particles. The secondary particles have an average particle diameter of 1-7 mu m. The parameter which shows the breadth of particle size distribution is 0.60 or less. The titanium exists only in the outer shell portion of the manganese nickel titanium composite hydroxide particle; and    (2) manufacture of positive electrode active material, which involves mixing lithium compound with respect to the manganese nickel titanium composite hydroxide particle to obtain lithium mixture, and baking the lithium mixture at 850-950 degrees C. The positive electrode active material comprises lithium-manganese-nickel-titanium complex oxide particle of cubic system which has spinel structure, and is of formula: LitMn2(1-x-y-z) Ni2xTi2yM2zO4.    t=0.96-1.20;    x=0.20-0.28;    y=0-0.05;    z=0-0.05;and    M=elements chosen from Mg, Ca, Ba, Sr, V, Fe, Cr, Co, Cu, Zr, Nb, Mo and W.