A process for producing 2,2′,3,3′,5,5′-hexamethyl-[1,1′-biphenyl]-4,4′-diol, which process comprises, while setting a pH of a reaction liquid containing an alkaline aqueous solution, a surfactant, a copper catalyst and 2,3,6-trimethylphenol during a reaction in the range of from 8 to 14 and controlling the variation range of the pH of the reaction liquid within ±1, oxidatively coupling the 2,3,6-trimethylphenol with an oxygen-containing gas, and a process for producing a bifunctional phenylene ether oligomer compound having a controlled average molecular weight, comprising carrying out oxidation polymerization under a proper oxygen concentration.