A process for producing a polyoxytetramethylene glycol or a copolymerized polyetherglycol by polymerizing tetrahydrofuran or a mixture of tetrahydrofuran with other cyclic ethers copolymerizable therewith, which comprises using a heteropoly-acid as a catalyst and permitting 0.1 to 15 mol of water per mol of the heteropolyacid to be present in the catalyst phase.The above-described polymer and copolymer are industrially useful polymers which can be used as the primary starting materials for polyurethanes to be used for a spandex and a synthetic leather, solvents, pressured fluids, etc.