A process for producing a bifunctional phenylene ether oligomer compound having a controlled average molecular weight, represented by the formula (5), comprising carrying out oxidation polymerization at an oxygen concentration lower than an oxygen concentration of an explosion limit of a solvent to be used by charging a reactor with a mixture containing a catalyst, an amine and a solvent in advance and then dropwise adding a mixture containing 2,2′,3,3′,5,5′-hexamethyl-(1,1′-biphenyl)-4,4′-diol of the following formula (2), a monovalent phenol of the following formula (6), an amine and a solvent to the mixture in the reactor, thereby producing a bifunctional phenylene ether oligomer of the formula (5),
- wherein, from a moment when the number average molecular weight of the bifunctional phenylene ether oligomer compound exceeds 500, the supply rate of the dropwise addition mixture is controlled such that the concentration of the monovalent phenol of the formula (6) in the reactor does not exceed 15% by weight based on the total amount of the above monovalent phenol, the bifunctional phenylene ether oligomer and the 2,2′,3,3′,5,5′-hexamethyl-(1,1′-biphenyl)-4,4′-diol [(6)/(5)+(2)+(6)<0.15],
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- in which R1 and R2 may be the same or different and are a halogen atom, an alkyl group having 6 or less carbon atoms or a phenyl group, R3 and R4 may be the same or different and are a hydrogen atom, a halogen atom, an alkyl group having 6 or less carbon atoms or a phenyl group, and each of m and n is an integer of 0 to 25 while at least one of m and n is not 0.