New block terpolymers of the poly[oxytetramethylene-block-(tetramethylene terephthalate)-block-lauroIactam] (PTMO-b-PBT-b-PA12) with potential applications as elastomers have been obtained by melt polycondensation of dimethyl terephthalate (DMT), 1,4-butanediol (BD-1,4), poly(oxytetramethylene)diol (PTMO), and α,ω-dicarboxylic-oligolaurolactam (PA 12) in the presence of magnesium-titanate organometallic complex as a catalyst. The influence of changes in the degree of polycondensation of poly(tetramethylene terephthalate) (PBT) on the structure and thermal and mechanical properties of the terpolymers has been determined by differential scanning calorimetry (DSC), dynamic mechanical thermal analysis (DMTA), and other standard physical methods. The system is characterized by a mutually disturbing effect of PA 12 and PBT segments on the phase structure of the terpolymers. Intermolecular interaction between these segments influences the elastomeric properties of these poly[ether-block-ester-block-amide] terpolymers.