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AbstractThe lateral shear margins of palaeo-ice stream beds are occasionally marked by large curvi-linear moraines but little work has addressed how they might form. In this paper we review the characteristics of 'lateral shear margin moraines' and present two quantitative models for their formation; (i) differential erosion rates related to lateral variations in the stream velocity; and (ii), lateral incursion from inter-stream ridges after the thinner stream retreats, where the shear margin moraine is consequently just a terminal moraine of the inter-stream ridge. Other possible mechanisms of formation are addressed qualitatively. Both of our quantitative theories are, in principle, feasible, but the incursion model is less plausible and inconsistent with observations. The differential erosion model can predict moraines tens of metres thick and several kilometres wide which can be formed in a thousand years. The width of the moraine depends on the competition between a term which varies across the ice-stream because it is dependent on ice velocity and which always causes erosion, and a term related to the local accumulation rate which causes erosion if is positive and deposition if negative. These terms combine to create the possibility of deposition at the shear margins of ice streams in ablation areas. The width of the moraine has a tendency to increase with the width of the stream. The conditions which permit shear margin moraines to form are quite constrained; too much ablation and deposition occurs everywhere rather than just near the lateral margins of the ice streams; too little ablation and there is erosion everywhere. This is consistent with the infrequent observations of lateral shear margin moraines.