The invention relates to a method for the single-step production of polytetrahydrofuran and/or tetrahydrofuran copolymers having an average molecular weight of 650 to 5000 daltons by polymerizing tetrahydrofuran on an acidic heterogeneous catalyst in the presence of at least one telogen and/or comonomer of the group of the alpha, omega diols, water, polytetrahydrofuran having a molecular weight of 200 to 700 daltons and/or of the cyclic ethers, characterized by a) removing the suspended and/or dissolved catalyst components and/or secondary products of the catalyst contained in the polymerization product, b) carrying out a separation in at least one distillation step from the resulting catalyst-free polymerization product to give a distillation product that contains the polymerization product and at least one tetrahydrofuran fraction, and returning at least part of the tetrahydrofuran fraction to the polymerization, and c) removing from the distillation residue of processing step b) the low-molecular polytetrahydrofuran and/or tetrahydrofuran copolymers that have an average molecular weight of 200 to 700 daltons, and obtaining a polytetrahydrofuran and/or tetrahydrofuran copolymer that has an average molecular weight of 650 to 5000 daltons.