The solidification of a binary system differs from a pure metal in that the latent heat effect no longer occurs at the melting point but rather in a freezing zone between the liquidus and solidus temperatures. Such solidification is analyzed from a heat-transfer point of view. The system considered occupies a semi-infinite region, is initially at the liquidus temperature, and at all subsequent times the surface temperature is considered constant; the fraction solid is assumed to be linear with distance within the freezing zone between the solidus and liquidus. The heat released during solidification is treated as a discontinuous heat generation. This corresponds to the nonequilibrium freezing of a eutectic system. The temperature distribution and thickness of each region are calculated as a function of time using the error function solution and the heat-balance integral; the results are given in graphical form.