The nucleation of rapidly solidified Au-19.25Ag-12.80Ge ternary eutectic alloy was analyzed and discussed according to the classical nucleation theory. Then the relationship between the incubation period of each phase and the melting temperature was obtained. The results show that for rapidly solidified Au-19.25Ag-12.80Ge brazing filler, the incubation period of AuAg solid solution is much shorter than that of Ge phase, and AuAg phase is precipitated preferentially as the main nucleation phase in the rapid solidification process. According to the time-dependent transient nucleation theory, the critical nucleation temperature, critical nucleation undercooling and critical nucleation number of the brazing filler were calculated under continuous cooling conditions. It can be seen that with increase of the cooling rate, the initial nucleation undercooling required to trigger melt nucleation increases, and the critical nucleation number increases substantially too.