The invention relates to a water-soluble, linear cyclodextrin copolymer for use as a medicament, the copolymer having a linear polymer backbone, which copolymer includes a plurality of cyclodextrin monomer moieties and linker moieties in the linear polymer backbone, wherein, unless the cyclodextrin monomer moiety or the linker moiety is present at the terminus of a polymer chain, each of the cyclodextrin monomer moieties is attached to two of the linker moieties and each of the linker moieties covalently links two cyclodextrin monomer moieties; and wherein the cyclodextrin monomer moieties are unsubstituted or substituted by groups that do not interfere with the copolymerization with the linker moiety.