Segmented block copolymers of polyisobutylene (PIB) and poly(butylene terephthalate) (PBT) were made by condensation polymerization of α,θ-di-anhydride telechelic PIB, with 1,4-butanediol and dimethyl terephthalate. The inherent viscosity of the polymers was between 0.35 and 2.0 dl g−1. The extractability of the polymers with hexane was studied. The thermal behaviour of these polymers was studied by differential scanning calorimetry and dynamic mechanical thermal analysis. PBT-b-PIB had a glass transition temperature of −62°C and a melting temperature of 200–220°C. A shear modulus was found which, at room temperature, increased from 0.4 to 900 MPa with increasing PBT content in the block copolymer. The degradation was followed by measuring the change of inherent viscosity during thermal and hydrolytic treatment. The PBT-b-PIB showed good resistance to thermal and hydrolytic degradation.