Provided are a positive electrode active material that can provide a nonaqueous electrolyte secondary battery having high energy density and excellent output characteristics, a nickel-manganese composite hydroxide as a precursor thereof, and methods for producing these. A nickel-manganese composite hydroxide is represented by General Formula (1): NixMnyMz(OH)2+α and contains a secondary particle formed of a plurality of flocculated primary particles. The nickel-manganese composite hydroxide has a half width of a diffraction peak of a (001) plane of at least 0.35° and up to 0.50° and has a degree of sparsity/density represented by [(a void area within the secondary particle/a cross section of the secondary particle)×100](%) within a range of greater than 10% and up to 25%.