The present invention provides a process for preparing polyoxyalkylene glycols of a certain molecular weight in one stage by copolymerizing tetrahydrofuran and alpha,omega-diols as the comonomer in the presence of a heteropolyacid and of a hydrocarbon, by distilling off a mixture of water and this hydrocarbon from the copolymerization, which comprises terminating the polymerization when this molecular weight is attained by adding water, comonomer, butanediol or butanediol-water mixtures.