Free eutectic growth and its competition with single-phase growth in solidification of undercooled near-eutectic alloys are not yet fully understood. In this paper, the historical development of eutectic growth models was reviewed. The LZ model of free eutectic growth was evaluated using recent data of eutectic growth velocities in an undercooled Ni81.3Sn18.7 eutectic composition. An excellent agreement was achieved between the LZ model and the data. Crystal growth velocities in off-eutectic Ni83Sn17 and Ni80Sn20 compositions were measured using a high-speed camera technique. The present data of the off-eutectic compositions and the recent data of the eutectic composition were modeled using the LZ model and the LKT/BCT model of free dendritic growth. The modeling revealed that the competition between the free eutectic growth and the single-phase growth is controlled by the highest interface temperature criterion. A coupled zone of the alpha-Ni-Ni3Sn eutectic was calculated using this criterion. The coupled zone agrees well with studies of solidified structures of undercooled samples.