The well-known problem of incipience of a mushy zone for binary melt solidification processes is solved with the aid of the Laplace transform in a laboratory coordinate system. The integral relations for the rate of solidification and the time of incipience of the mushy zone are derived when crystallization proceeds near a cooling wall. The last assumption is confirmed by numerical calculations and by the relations obtained. In other words, a mush appears ahead of the solidification front at the initial stage of crystallization (when the front moves toward the binary melt near the cooling wall). Thus, the time when the classical description of crystallization by means of the Stefan thermodiffusion model becomes incorrect and when the mushy region appears due to the concentrational (constitutional) supercooling is found. ©2003 Begell House, Inc.