Rock glaciers—ice-rich creeping landforms typical of permafrost mountain ranges—can develop an anomalous landslide-like behaviour called destabilisation. This behaviour is characterised by failure mechanisms (including cracks and crevasses) and increases in displacement rates by one to two orders of magnitude. Existing studies of this phenomenon have been limited to a small number of landforms and short time spans. Here, we systematically investigate the evolution of rock glacier kinematics over the past seven decades for the entire French Alps by combining observations of landform features indicative of the onset of destabilisation with data on displacements rates using aerial orthoimagery. We show that rock glacier velocities have significantly increased since the 1990s, concurrent with the development of destabilisation in 18 landforms that represent 5% of the 337 active rock glaciers. This pattern of activity correlates with rising air temperatures in the region, which suggests that a warming climate may play a role in this process.