Unexpected surface level and discharge oscillations have been reported in tributaries of the Yellow River in China. The oscillations typically occur during the declining part of long-period flood waves, when the flows carry extremely high concentrations of very fine sediment. The oscillations reportedly cannot be explained by analysis techniques developed for flows of clear water. An analysis is presented in which the flowing material is modeled as a Bingham plastic. The analysis is based on the depth-integrated mass and momentum equations, with a simplified representation of boundary friction. With reasonable values of the parameters involved, the analysis indicates that the existing qualitative observations of surface and discharge oscillations can be explained by a linear instability to surface waves. Although based on a Bingham plastic model, the qualitative conclusions can be extended to more general types of constitutive behavior. ¿ American Geophysical Union 1987