The invention provides a cyclodextrin-containing polymer comprising one or more cyclodextrin residues. The polymer is selected from a peptide, a polypeptide, an oligonucleotide or a polynucleotide or a mixture thereof. The peptide or polypeptide has at least one amino acid residue containing a functional side group and at least one of the cyclodextrin residues is covalently linked to the functional side group of the amino acid residue of said peptide or polypeptide or to the sugar moiety of a nucleotide residue of the oligonucleotide or polynucleotide.