A nonsteady model of an ice stream flowing on deforming till shows that the system responds rapidly and in a stable manner to reasonable marginal perturbations. For the model we require one-dimensional flow and continuity of ice and till, we assume linear viscous till rheology and balence between the driving stress for ice flow and the resistive stress at the bed. This allows us to write coupled equations for the time rate of change of the ice thickness and the till thickness in terms of these thicknesses and the till viscosity. An analytic, steady state solution for ice stream B, West Antarctica, shows that till viscosity decreases slowly downstream, probably in response to decreasing effective pressure downstream. Nonsteady numerical experiments with fixed ice thicknesses at the ends show that a marginal perturbation causes a wave of adjustment to travel the length of the ice stream in about 50 years, with a new steady state in about 200 years. Changes in till thickness tends to moderate perturbations in the ice and thus stabilize the system. ¿ American Geophysical Union 1987