Cationic polymerizations of β-propriolactone (Prop), -caprolactone (Capr), and glycolide (Glyc) were initiated by various alkylsulfonates, such as methyl fluorosulfate, ethyl fluorosulfate, methyl trifluoromethanesulfonate (triflate), methyl methanesulfonate, methyl p-nitrobenzene sulfonate, γ-propane sultone, and δ-butane sultone. Systematic variation of reaction time and temperature revealed that only methyl fluorosulfate and methyl triflate can give high yields, yet the temperature must be kept in a narrow range (50 ± 10°C). Due to the living character of the cationic endgroups, high temperatures may cause rapid degradation of the initially formed polylactones. However, at appropriate temperatures, the living chain ends permit the synthesis of block copolyesters. The sequences of the two-block copolyesters built up of Prop and Glyc or Capr and Glyc units were characterized by means of13C-NMR spectra and compared to random copolylactones. The DSC curves of the two-block copolyesters display the expected two melting endotherms, whereas those of the random copolyesters do not.