Two new monomers based on R-terpineol were prepared, allyl R-terpineol ether epoxide (III) and 1-propenyl ether R-terpineol epoxide (IV). The photoinitiated cationic polymerizations of these two monomers as well as two model compounds, 1-propenyl R-terpineol ether and methyl R-terpineol ether epoxide, were studied using real-time infrared spectroscopy. Surprisingly, the rates of epoxide ring-opening polymerization of both monomers were greatly enhanced as compared to the model compounds. At the same time, the rate of polymerization of the 1-propenyl ether groups in IV was depressed. Two different mechanisms which involve the free radical induced decomposition of the diaryliodonium salt photoinitiator were proposed to explain the rate acceleration effects.