Cu-Bi alloy with high Bi content can be used for thermal surge protection and energy storage. For these applications, creep at high temperatures, including temperatures above the melting temperature of Bi, Tm,Bi, becomes important. Accordingly, the creep behavior of Cu-Bi alloys, comprising 30 and 40 vol pct Bi, was studied under compression at temperatures above and below Tm,Bi. At 200 °C, which is below Tm,Bi, Cu-Bi showed a stress exponent of ~ 4 at high stresses and ~ 1 at low stresses. Finite element analysis revealed that the creep behavior of Cu-Bi at 200 °C was predominantly governed by Bi. On the other hand, at temperatures higher than Tm,Bi, Cu-Bi showed a short transient stage at high stresses, followed by sudden failure of the material. However, at low stresses, the sample first continued to expand and then started to accumulate compressive strain. A qualitative model based on interaction between liquid Bi and Cu is developed to explain the observed creep behavior at temperatures higher than Tm,Bi. The results obtained here shed light on the creep behavior of alloys with constituents having significantly different creep behavior and containing a non-reacting liquid phase.