New poly(ester-b-aliphatic) multiblock elastomers contg. poly(ethylene terephthalate), poly(trimethylene terephthalate) and poly(butylene terephthalate) hard segments and hydrophobic soft linoleic alc. dimer segments were prepd. and studied by H-1 NMR and FTIR methods to confirme their assumed chem. structures and by DSC and DMTA methods to det. the phase sepn. and thermal properties.