The behavior of superconducting NbTi wires under dynamic mechanical stress was investigated. Instabilities on the stress‐strain curve (serrated yielding) were found connected with local transition into the normal state. With applied field and transport current, NbTi conductors with and without copper matrix showed a training behavior. This means that the normal transitions occurred at successively higher stress levels. Mechanisms proposed so far, such as serrated yielding of NbTi or deformation of the copper matrix in compound conductors, do not seem to explain the training of superconducting magnets.