The compounds bis(phenyhmethyl) cis-cyclobutene-3,4-dicarboxylate (1) and cis-3,4-bis(2-oxa-3-phenylpropyl)cyclobutene (2) were polymerized by ring-opening metathesis polymerizations using Mo(CHC(CH3)(2)R(1))(NC6H3-2,6-diisopropyl)(OR(2))(2) (R(1) = Ph, R(2) = C(CH3)3, I; R(1) = CH3, R(2) = C(CF3)(2)CH3, II) as the initiator. For I as initiator, no chain termination or chain transfer processes were observed during the lifetime of the polymerization, showing that the polymerizations of 1 and 2 by I are living. Block copolymers containing 1 and 2 and diethyl cis-cyclobutene-3,4-dicarboxylate (5) were synthesized. The double bonds of the poly-2 and poly-3 ranged from 70% trans to 92% cis depending on the initiator and monomer used. Poly-1 and poly-2 were treated with iodotrimethylsilane and converted to the acid-functionalized and alcohol-functionalized poly-4 and poly-6, respectively. Block copolymers were treated with iodotrimethylsilane and converted to materials with blocks Gearing protic functionalities and blocks bearing polar aprotic groups.