NOVELTY - Positive active material particulate powder contains secondary particles as cores and lithium-manganese compound particles containing lithium-manganese-nickel oxide and lithium-manganese-iron oxide and which covers or exist in surface of the secondary particles or in the vicinity of the surface. The average particle diameter of secondary particles of positive electrode active material particulate powder is 1.1 times or more average particle diameter of secondary particles used as core. The content of lithium-manganese compound particles is 0.5-20 weight%.    USE - Positive active material particulate powder is used for nonaqueous electrolyte secondary battery (claimed) used for hybrid vehicle and electric vehicle.    ADVANTAGE - The nonaqueous electrolyte secondary battery containing the positive active material particulate powder has excellent charging and discharging characteristics.    DETAILED DESCRIPTION - Positive active material particulate powder contains secondary particles as cores and lithium-manganese compound particles containing lithium-manganese-nickel oxide of formula: LixMn2-yNiyO4 (I) and/or lithium-manganese-iron oxide of formula: LizMn1-nFenPO4 (II), where x is 0.95-1.1, y is 0.45-0.55, z is 0.98-1.1 and n is 0-0.3 excluding 0 and which covers or exist in surface of the secondary particles or in the vicinity of the surface. The secondary particles are lithium-manganese composite oxide particles comprising compound having crystal system belonging to the space group R-3m and crystal system belonging to the space group C2/m. The X-ray powder diffraction pattern of secondary particles has relative intensity ratio of the intensity (a) of the maximum diffraction peak at 2( theta ) (20.8 plus minus 1 degrees ) to the intensity (b) of the maximum diffraction peak at 2( theta )(18.6 plus minus 1 degrees ) of 0.02-0.5, when examined with copper-K( alpha ) line. The average particle diameter of secondary particles of positive electrode active material particulate powder is 1.1 times or more average particle diameter of secondary particles used as core. The content of lithium-manganese compound particles is 0.5-20 weight%. An INDEPENDENT CLAIM is included for manufacture of positive active material particulate powder.