The fatigue behaviour of poly(aliphatic/aromatic-ester) (PED) multiblock copolymers has been evaluated using the hysteresis loop method. Stepwise increasing strain test (SIST) was performed at a frequency of 1 Hz. The strain levels were varied with increasing extension steps: 3, 5, 10, 15, 20, 25 and 30% of the initial strain, while minimum stress has been set at a constant value of 0.1 MPa. It has been found that soft PEDs show a very good stress relaxation due to the fact that they contain high amounts of the amorphous phase and their soft segments do not crystallize. PED copolymers, especially those containing low amounts of crystalline hard domains showed very good damping properties at small strain levels. It has also been found that PED's ability to store and dissipate energy is a function of the hard segment concentration. This method proved to be a useful tool for determining the changes in the material properties of PEDs and other thermoplastic elastomers during deformation. (C) 2003 Elsevier Ltd. All rights reserved.