SOLID amorphous alloys can be made by a wide variety of techniques1. Of these, rapid liquid quenching and solid-state amorphization (SSA) in annealed multilayers can be most readily analysed according to a condensed-phase equilibrium diagram for the alloy. Here we consider how the phase equilibria in eutectic systems are affected by the interaction of the liquid components. We use such considerations to show the link between two apparently distinct types of alloy system: one capable of exhibiting SSA, in which there are compounds and a deep metastable eutectic; the other not capable of SSA, but capable of glass formation by rapid liquid quenching, in which there is only a stable eutectic. In alloys of intermediate type we propose that there exists a novel transformation, the inverse eutectic transition, which is a special case of a peritectoid transformation (two solid phases transforming to a single solid phase on cooling) in which the product phase is amorphous.