The self-similar solidification process of in alloy from a cooled boundary is Studied on the basis of two models with a planar fro lit a lid Mushy layer. Approximate and exact analytical Solutions Of the process, which demonstrate unusual dynamics near the point of constiututional Supercooling, are found. The rate of solidification and front position of the solid/mush boundary (parabolic growth rate constant) are expressed in an explicit form in the case of slow dynamics of this boundary. The theory under consideration is in a good agreement with experimental and numerical studies carried out by Huppert and Worster for ice growing from aqueous salt solutions. (c) 2005 Elsevier Ltd. All rights reserved.