The invention provides a cross-linked poly-&egr;-lysine polymer. The poly-&egr;-lysine and cross linker are linked by amide bonds and may the cross linker has at least two functional groups capable of reacting with an alpha carbon amine of poly-&egr;-lysine. The polymer is suitably insoluble in water and other solvents and is provided in particulate form. The invention provides a particulate support comprising the cross-linked poly-&egr;-lysine polymer and the polymer may provide the particle itself or be coated on a particle for example silica. The polymer is useful in a wide range of applications including wound treatment, as a medical diagnostic comprising a particulate support and a functional material bound or retained by the support and solid phase synthesis of peptides, oligonucleotides, oligosaccharides, immobilisation of species, cell culturing and in chromatographic separation.