Abstract: 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.