Propylene oxide (PO) and CO2 are terpolymerized with 5-norbornene-2,3-dicarboxylic anhydride (NA) or tetrahydrophthalic anhydride (THPA) under the action of a zinc glutarate catalyst. NMR analysis confirms that the anhydrides are comonomers and are inserted to give ester entities. It was observed that the molecular mass of the terpolymers is higher and the content of the backbiting product cyclic propylene carbonate (cPC) is lower in comparison to PO/CO2 copolymerizations, and that they correlate with each other. Especially NA is suited to decrease the amount of byproduct cPC at initial concentrations lower than 0.5 mol% anhydride (relative to PO). The reactivity ratios of CO2 and maleic anhydride (MA), phthalic anhydride (PA), THPA and NA are 0.72, 0.23, 0.041 and 0.027 resp., showing that NA is not readily incorporated. The reduction of backbiting is thus related to the observed increase in molecular mass resulting from a lower rate of termination which, in turn, would result from an interaction of anhydride with the catalyst surface. The higher molecular mass and lower cPC content results in materials with a higher glass transition temperature, higher yield strength, elastic modulus and stress at break.