The development of new strategies for producing polyesters can expand the category of biodegradable materials. Here, we disclose the alternating copolymerization of cyclic acetals (made from formaldehyde and diols) and anhydrides for the first time, using 5 cyclic acetals and 9 anhydrides to afford 45 unprecedented polyesters. At a wide range of reaction temperatures (25 to 140 °C), diverse metal-free Lewis/Brønsted acids are highly active catalysts for these copolymerizations via the cationic mechanism. Of interest, kinetic studies indicate that the copolymerization of cyclic acetals and anhydrides shifts the chemical equilibrium of "cyclic acetals * * polyacetals" to the left, thus yielding polyesters with up to > 99 % alternating degree. The obtained polyesters possess high oxygen content ([O] : [C] up to 6 : 7), molecular weights of 2.0-33.3 kDa, narrow polydispersities of 1.2-1.5, low glass transition temperatures (À 64 to À 27 °C), as well as high decomposition temperatures (275 to 324 °C).