Terpolymers of lactide, glycolide and trimethylene carbonate initiated on zirconium acetylacetonate (IV) exhibit shape-memory behaviors in the range of body temperature when appropriate monomer composition and characterizing conditions are applied. In this paper, the procedure of characterizing these terpolymers by means of nuclear magnetic resonance spectroscopy is presented. The 1H and 13C NMR spectra allow to characterize the chain microstructure of these polyester-carbonates in spite of overlapping resonance signals due to the possibility of forming different co-monomeric sequences. Detailed assignment was given for spectral lines in proton and carbon spectra recorded in polar and non-polar deuterated solvents. For quantitative analysis, equations for calculations of average block lengths, long and mixed glycolidyl, lactidyl and carbonate blocks as well as formulas allowing to investigate intramolecular transestrification processes were elaborated.