The formation of micro-sized droplets in the matrix of the primary phase of Ag-Ge alloys and their undercooling behaviour were investigated. Thermal cycling consisted in equilibration of hypoeutectic alloys near the eutectic temperature in the two-phase liquid-solid region followed by up-quenching of alloys at 30-50 degrees C above the eutectic temperature and their subsequent slow cooling. A wide size range of droplets was generated in the matrix of the silver-rich phase by repeated thermal cycling of the alloy. During slow cooling, droplets of silver-rich liquid exhibited a maximum undercooling of 81 degrees C below the eutectic temperature. Examination of the solidification structure of the undercooled alloys, by X-ray diffraction, polarized light microscopy and electron probe micro analysis techniques, indicated the presence of a metastable phase. The mechanism of formation of droplets and the nature of non-equilibrium solidification of the undercooled melt of silver-germanium alloys, are discussed.