One aspect of the invention relates to a biocompatible, covalently cross-linked, polymer that is obtained by reacting an electrophilically activated polyoxazoline (EL-POX) with a nucleophilic cross-linking agent, said electrophilically activated POX comprising m electrophilic groups; and said nucleophilic cross-linking agent comprising n nucleophilic groups, wherein the m electrophilic groups are capable of reaction with the n nucleophilic groups to form covalent bonds; wherein m≧2, n≧2 and m+n≧5; wherein at least one of the m electrophilic groups is a pendant electrophilic group and/or wherein m≧3; and wherein the EL-POX comprises an excess amount of electrophilic groups relative to the amount of nucleophilic groups contained in the nucleophilic cross-linking agent. The invention further relates to biocompatible medical products comprising such a cross-linked POX-polymer. Also provided is a kit for producing a biocompatible, cross-linked POX-polymer. The invention further provides a tissue adhesive medical product comprising at least 1% by weight of dry matter of EL-POX, said EL-POX comprising at least 2 electrophilic groups, including at least one pendant electrophilic group. The polymers according to the invention have excellent implant and/or sealing characteristics.