A systematic study of the solidification mechanisms of binary Sn-Cu and ternary Sn-Cu-Ni alloys has been carried out. It is found that Sn-Cu is a weakly-irregular eutectic system with Cu6Sn5 as the leading phase. Interestingly, two different eutectic morphologies (coarse and fine) are found to grow simultaneously during eutectic solidification. When the growth rate or composition is changed, the eutectic interface breaks down into a cellular eutectic with the fine eutectic in the center of the cells and the coarse one at the cell boundaries. The mechanisms responsible for these phenomena are discussed in conjunction with the beneficial effect of Ni additions to the Sn-Cu solder.