Synthesis and characterization of a new series of low molecular weight (MW = 500-3000) OH-terminated linear aliphatic unsaturated polyesters based on cis-2-butene-1,4-diol and oxalic to sebacic acid were investigated. Direct polycondensation and transesterification methods were used for the syntheses. The latter was recognized to be the preferable method due to its lower reaction temperature and time, lower diol/diacid ratio, absence of decarboxylation, and formation of a product with low polydispersity ((M) over bar(w)/(M) over bar(n) = 1.3-2.7). Elemental analysis, GPC, FTIR, H-1-NMR, DSC, and WAXD were used for the investigations. A segmented polyurethane based on poly (cis-2-butylene adipate) glycol was also synthesized and spectroscopically identified.