Novel hyperbranched polymers were synthesized in a high yield without gelation through the free-radical alternating copolymerization of an AB/B' (allyloxy maleic acid/maleic anhydride) system, in which group B and monomer B' both could only alternately polymerize with group A. The arm number of the produced highly branched polymers was equal to the product of the linear chain length and the probability of pendent B groups being growing centers. The molecular weight of these novel hyperbranched polymers increased with increasing initiator concentration and prolonged polymerization times. The AB/B' system, used as described, provides a new general methodology for highly branched and functional polymers.