A biocompatible, covalently cross-linked, polymer that is obtained by reacting an electrophilically activated polyoxazoline (EL-PDX) with a nucleophilic cross-linking agent is disclosed. The EL-PDX comprises m electrophilic groups; and the nucleophilic cross-linking agent comprises n nucleophilic groups, wherein the m electrophilic groups are capable of reacting 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-PDX comprises an excess amount of electrophilic groups relative to the amount of nucleophilic groups contained in the nucleophilic cross-linking agent. Biocompatible medical products and kits comprising the cross-linked PDX-polymers are also disclosed.