Polyoxazolines having the structural formula: ##STR1## wherein R is phenylene or alkylene containing 2 to 18 carbon atoms, R.sup.2 is C.sub.1-4 alkyl and R.sub.1 is selected from the group consisting of C.sub.1-12 alkyl, vinyl, isopropylidene, pentafluoroethyl, phenyl, hydroxyphenyl which is optionally interrupted by up to 20 ethylene oxide groups, C.sub.1-2 -alkoxyphenyl which is optionally interrupted by up to 20 ethylene oxide groups and .paren open-st.CH.sub.2 CH.sub.2 --O.paren close-st..sub.r CH.sub.3 in which r ranges from 1-20, X is NH.sub.2 or OH, n ranges from 2 to 50 and m ranges from 0 to 50, wherein R.sub.1 is hydroxyphenyl optionally interrupted by up to 20 ethylene oxide groups only when X is NH.sub.2, are polymerizable to form hyperbranched polymers which have a number average molecular weight ranging from 5,000 to 150,000, a weight average molecular weight ranging from 5,500 to 5,000,000 and a polydispersity ranging from 1.1 to 300 and which are very polar and highly wettable and are useful as adhesives, biodegradable materials, biomaterials, carriers for chemicals, carriers for image contrast agents, coatings, components of blends, components of medical imaging formulations, crosslinkers, dispersants, drug carriers, imaging materials, resists for lighography, slow release agents, vectors for gene therapy, and viscosity modifiers.