Nonisocyanate polyurethane materials with pending alcohol groups in the polymeric chain were synthesized by polyaddition reaction of bis(cyclic carbonates) onto diamines. For the platform molecule, 1,4-butanediol bis(glycidyl ether carbonate) (BGBC, 1) was used. The polyaddition reaction of 1 onto a wide range of diamines with different electronic and physical properties was explored. All PHUs were obtained quantitatively after 16 h at 80 °C temperature in MeCN as solvent. The low nucleophilicity of L-lysine has proven unable to ring-open the cyclic carbonate and, thus, no reaction occurred. The addition of DBU or TBD as the catalyst was tested and allows the obtention of the desired PHU. However, the presence of strong bases also led to the formation of polyurea fragments in the new PHU. The different poly(hydroxyurethane) materials were characterized using a wide range of spectroscopic techniques such as NMR, IR, MALDI-ToF, and using GPC studies. The thermal properties of the NIPUs were investigated by DSC and TGA analyses. Moreover, reactions employing different monomer ratios were performed, obtaining novel hydroxycarbamate compounds. Finally, sequential and one-pot experiments were also carried out to synthesize the PHUs polymers in one-step reaction.