Abstract: Disclosed is a polymer of the formula I: wherein: Z is —O— or —NH—; R1 represents a non-functional backbone of a hydroxy acid or amino acid derived from a cyclic ester or diester or cyclic amide or diamide monomer (A); R2 represents a non-functional chain derived from an epoxide monomer (B), said chain ending with a graftable hydroxy or carboxylic group; n is the number of units derived from the monomers (A); m is the number of units derived from the monomers (B); and x is equal to n+m, the ratio m/x ranging from 0.005 to 0.30. Also disclosed is a process of preparing this functionalizable polymer to the hydroxy or carboxylic groups of which can be grafted a compound selected from the group consisting of: ligands specific to cellular receptors, such as Selectine E; lipids; peptides; polyethers; polyacrylates; natural polymers; polyosides; antigens or antibodies; salen; and cyclodextrins. The so grafted polymer can be used as carried or excipient in the biomedical and pharmaceutical fields.