In the study presented, the damping capacity of shape memory alloys in the austenitic range was considered. The investigations on the dynamic behaviour of pseudoelastic shape memory alloys start with tensile tests on NiTi specimens at frequencies of up to 4 Hz. These experiments show that the beginning of the transformation process is more difficult to observe and that the critical stress value for the transition to martensite becomes obviously smaller at higher strain rates. Furthermore, the area of the hysteresis loop is reduced with increasing strain rate. The damping behaviours of NiTi and steel are directly compared in experiments on a pre-strained string. The system is excited by hammer impact as well as by an electrodynamic shaker. It is pointed out that the damping capacity is highly dependent on the vibration amplitude. Further experiments are performed with coil springs made from NiTi and steel. A stiff beam on which additional masses are mounted is supported by two coil springs so that the whole assembly can be considered as a spring-mass system. The results which were obtained in the string experiments are verified by these investigations.