In 1973, surface velocities were measured for the first time on an unstable hanging glacier to predict its collapse. The observed velocities have been shown to increase as a power-law function of time up to infinity at the theoretical time of failure (known as ‘finite time singularity’). This is the characteristic signature of critical phenomena and has been observed in the case of various other naturally occurring ruptures such as earthquakes, landslides and snow avalanches. Recent velocity measurements performed on Weisshorn and Mönch hanging glaciers, Switzerland, confirmed this behaviour, while log-periodic oscillations superimposed on this general acceleration were also detected. Despite different rupture mechanisms in both cases, the log frequency of the oscillations is shown to be the same. The seismic activity was recorded near the unstable Weisshorn hanging glacier, simultaneously with the velocity measurements. Results show dramatically increasing icequake activity 3 days before the final collapse. Combined motion–seismic monitoring seems to be a promising way to accurately predict the breaking-off of hanging glaciers. Such a combined analysis is also useful for capturing the physical mechanisms of rupture in natural heterogeneous materials.