Polycondensation of p-xylylene dibromide and M2CO3 (M = Li, Na, K, Rb, and Cs) catalyzed by CuI gives polymer 1 which contains the p-xylylene carbonate structural unit, -CH2C6H4CH2O(C=O)O-(a), and the p-xylylene oxide unit, -CH2C6H4CH2O- (b), randomly in the polymer chain. The use of Rb2CO3 and Cs2CO3 as the source of the carbonate group increases the yield of the polymer. Cu compounds including [Cu(C=CPh)(PPh3)](4), Cu(C=CC3H7), CuBr, CuBr2, and CuBr2(phen)(n) (phen = 1, 10-phenanthroline, n = 1,2) also catalyze the polycondensation to give a product rich in unit a. The polycondensation catalyzed by alkynylcopper(I) complexes with or without addition of 1, 10-phenanthroline gives a polymer with a high content of unit a (> 95%). Polymer 1 possesses CH2OH terminal groups which are identified by H-1 and C-13{H-1} NMR as well as by reaction with an alkyl isocyanate. Reactions of 1 with diisocyanates such as 4-methyl-1, 3-benzenediisocyanate, m-xylylene diisocyanate, and 1, 6-hexanediisocyanate cause the polyaddition of 1 to the N=C=O bonds resulting in new polymers containing the macromonomer units bonded through bisurethane groups.