The present invention provides a process for preparing mono- or diesters of polytetrahydrofuran or of tetrahydrofuran copolymers by polymerizing tetrahydrofuran in the presence of at least one telogen and/or of a comonomer over an acidic catalyst, wherein the polymerization reactor is started up using a mixture of polytetrahydrofuran, the mono- or diesters of polytetrahydrofuran and/or of the THF copolymers, tetrahydrofuran, any comonomer and at least one carboxylic acid and/or one carboxylic anhydride.