The invention provides a process for preparing polytetrahydrofuran, tetrahydrofuran copolymers, their monoesters or diesters and the monoesters or diesters of polytetrahydrofuran having a low color number in the presence of a catalyst, which comprises converting crude tetrahydrofuran which has been prepared in a manner per se into pure tetrahydrofuran by distillation, subsequently subjecting the latter to essentially complete hydrogenation and using the high-purity tetrahydrofuran obtained in this way for the polymerization directly after its preparation.