NOVELTY - Positive-electrode active-material particles and self-cohesive electroconductive substance (I) are mixed in solvent (I), to obtain slurry (I). Slurry (II) is obtained by mixing the active-material particles, electroconductive substance (I), a binder, and solvent (II). Slurry (II) is mixed such that the rheology characteristics of slurry (II) measured using rheology measuring apparatus shows a gradient of -0.3 to 0.3 with respect to a shear rate of 0.001-0.1 second-1 and shear stress of 1000-40000 mPa.    USE - Manufacture of composition for positive electrodes of non-aqueous electrolyte secondary batteries (all claimed) e.g. lithium ion secondary battery and nickel-cadmium secondary battery. Uses include but are not limited to notebook personal computers, portable audio players, mobile telephones, vacuum cleaners, cordless electric tools, electric vehicles, hybrid cars, and fuel-cell vehicles.    ADVANTAGE - The method enables manufacture of composition which provides positive electrodes which form batteries with reduced internal resistance, due to sharp reduction in diffusion of active-material ion.    DETAILED DESCRIPTION - Positive-electrode active-material particles and self-cohesive electroconductive substance (I) are mixed in solvent (I), to obtain slurry (I). Slurry (II) is obtained by mixing the active-material particles, electroconductive substance (I), a binder, and solvent (II). The active-material particles have a BET specific surface area of 1-6 m2/g, and a total pore volume of 0.1-1 cc/g as measured using a mercury porosimeter. Peak pore diameter (I) which gives the greatest differential pore volume value exists in a pore diameter of 0.01-8 mu m. Peak pore diameter (II) which gives 5% or more of differential pore volume value of the greatest differential pore volume value exists in a pore diameter less than diameter (I) by 0.01 mu m or more. The average particle diameter as measured by laser diffraction/scattering type particle-size distribution measurement, is diameter (I) to 20 mu m. The average particle diameter when mixing electroconductive substance (I) with the active-material particles is 1-50 mu m. The content of electroconductive substance (I) in slurry (I) is 3-20 parts weight with respect to 100 parts weight of active-material particles. Slurry (II) is mixed such that the rheology characteristics of slurry (II) measured using rheology measuring apparatus shows a gradient of -0.3 to 0.3 with respect to a shear rate of 0.001-0.1 second-1 and shear stress of 1000-40000 mPa. An INDEPENDENT CLAIM is included for slurry.