Display omitted •Synthesis of a new 5-membered bis(cyclic carbonate) based on D-mannitol.•Synthesis of new 6-membered cyclic carbonate based on di(trimethylolpropane).•Poly(carbonate-urethane) networks synthesized without the use of isocyanates. Bis(cyclic carbonate)s based on sugar alcohols such as d-mannitol, d-sorbitol as well as di(trimethylolpropane) were used as monomers for preparation of a variety of crosslinked poly(carbonate-urethane)s (PCUs), which do not require either phosgene or toxic isocyanate monomers. In the approach proposed by us, crosslinked structure of poly(carbonate-urethane)s are obtained in the reaction of amine-terminated oligo(hydroxy-urethane)s with six-membered bis(cyclic carbonate) and then by polymerization of residual six-membered cyclic carbonate ending groups. Depending on the aliphatic diamine used as well as the molar ratio of five- to six-membered bis(cyclic carbonate)s the obtained non-isocyanates polyurethanes (NIPUs) were characterized by elastomeric or rigid properties.