Coagulated particles of nickel-cobalt-manganese hydroxide wherein primary particles are coagulated to form secondary particles are synthesized by allowing an aqueous solution of a nickel-cobalt-manganese salt, an aqueous solution of an alkali-metal hydroxide, and an ammonium-ion donor to react under specific conditions; and a lithium-nickel-cobalt-manganese-containing composite oxide represented by a general formula, Li.sub.pNi.sub.xMn.sub.1-x-yCo.sub.yO.sub.2-qF.sub.q (where 0.98.ltoreq.p.ltoreq.1.07, 0.3.ltoreq.x.ltoreq.0.5, 0.1.ltoreq.y.ltoreq.0.38, and 0.ltoreq.q.ltoreq.0.05), which is a positive electrode active material for a lithium secondary cell having a wide usable voltage range, a charge-discharge cycle durability, a high capacity and high safety, is obtained by dry-blending coagulated particles of nickel-cobalt-manganese composite oxyhydroxide formed by making an oxidant to act on the coagulated particles with a lithium salt, and firing the mixture in an oxygen-containing atmosphere.