Dislocation lines in a crystal close to a bulk phase transition can be coat
ed by nuclei of a new phase which for a moving dislocation gives rise to a
viscous friction force. In some range of the material parameters this force
leads to a dynamic instability of the defect line, resulting from an intri
cate interplay between the shape fluctuations of the defect and the amplitu
de fluctuations of the nucleus. The instability shows up in the linear resp
onse of the dislocation to a periodic change of the driving force and in th
e structure factor of the order-parameter fluctuations of the nucleus.