Observations of unusual surface level oscillations on the sediment-laden Yellow River of China, have led to the suggestion that the oscillations arise from a free surface instability peculiar to fluids having the constitutive relation of a Bingham plastic (i.e., possessing a finite yield stress). A model has been proposed in which free surface flows of Bingham plastics appear unstable at conditions for which the corresponding flow of clear water would be stable. We argue here that gravity driven Bingham plastics are, in fact, stable to free surface oscillations and that consequently the Yellow River oscillations most likely do not stem from a simple surface instability. ¿ American Geophysical Union 1990