Contrary to what has recently been assumed in modeling the proposed deforming bed mechanism for the rapid motion of Antarctic ice streams, the rheology of water saturated till is probably highly nonlinear, according to information from soil mechanics and preliminary experiments on till from the base of Ice Stream B. The equivalent flow law exponent n is probably as high as ~100, and the nonlinearities of the shear stress and effective pressure dependences are closely linked. The high nonlinearity has important consequences for the deforming bed mechanism. A flow system operating by this mechanism can be unstable as a result of feedback from the generation of basal water by shear heating of basal till. The short-term feedback effect is analyzed for a perturbation in a model ice stream in which the basal meltwater is transported through a distributed system of narrow gap-conduits at the ice-till interface. Although the analysis is approximate and some of the system parameters are poorly known, the results suggest that the deforming bed mechanism is unstable for n>~20. The apparent lack of such an instability in the currently active ice streams implies that their motion is controlled not by the deforming bed mechanism but by some other as yet unidentified mechanism. ¿American Geophysical Union 1991