Melts of the eutectic alloy Ag‐39.9 at. %Cu were cooled below the liquidus temperature by the glass flux method. The solidification behavior was followed by measuring the temperature change (recalescence), and the resulting microstructures were investigated by optical and electron microscopy. Up to a certain critical undercooling &Dgr;T*≊76 K, the recalescence rate is less than 100 K s−1, and a feathery, lamellar microstructure is formed, with typically one or two growth centers. When the undercooling exceeds &Dgr;T*, a sudden increase in the recalescence rate (up to 104K s−1) is observed, and the microstructure consists of a dendritic, irregular two‐phase component surrounded by a lamellar eutectic. The critical undercooling temperature coincides with the temperature (T0) at which the Gibbs free energies of the liquid and the supersaturated Ag‐Cu solid solution are equal. The critical behavior is therefore thought to be due to the formation of this metastable phase. A model is proposed to explain the observed behavior and microstructures.