A system of depth-integrated equations, forming a rather primitive mathematical model of horizontally two-dimensional (2DH) bed evolutions in shallow water, is analyzed using characteristics theory. The analysis shows that the solution of this system exhibits an essentially two-dimensional propagation character, with bottom disturbances traveling in other directions than the current velocity and the sediment transport. The results of this analysis are verified by numerical experiments and interpreted physically. Their relevance for numerical modeling of 2DH morphological processes in shallow water is discussed, and their occurrence and recognizability in natural situations is checked by a qualitative comparison with field observations. ¿American Geophysical Union 1987