Polytetrahydrofuran, polytetrahydrofuran copolymers, diesters or monoesters of these polymers are prepared by polymerization of tetrahydrofuran in the presence of at least one telogen and/or comonomer, which is in the form of shaped catalyst bodies or catalyst particles having a volume of the individual shape of the body or particle of at least 0.05 mm3, preferably at least 0.2 mm3, in particular 1 mm3, and has at least one of the features a) and b): a) a pore radius distribution having at least one maximum in the pore radius range from 100 to 5000 Å, b) a pore volume of catalyst pores having radii of 200–3000 Å of greater than 0.05 cm3/g and/or a pore volume of pores having radii of 200–5000 Å of greater than 0.075 cm3/g and/or a pore volume of pores having radii of >200 Å of greater than 0.1 cm3/g.