Provided are a positive electrode active material with which a nonaqueous electrolyte secondary battery having a high energy density can be obtained, a nickel-manganese composite hydroxide suitable as a precursor of the positive electrode active material, and production methods capable of easily producing these in an industrial scale. Provided is a nickel-manganese composite hydroxide represented by General Formula (1): NixMnyMz(OH)2+α and containing 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 obtained by X-ray diffraction measurement of at least 0.10° and up to 0.40° and has a degree of sparsity/density represented by [(void area within secondary particle/cross section of secondary particle)×100](%) of at least 0.5% and up to 10%. Also provided is a production method of the nickel-manganese composite hydroxide.