A new class of high-entropy alloys (HEAs), called eutectic high-entropy alloys (EHEAs), has been developed to address the challenges of achieving both high strength and ductility in high-temperature materials. This study introduces a novel strategy using the eutectic alloy concept to design HEAs with a microstructure composed of alternating soft face-centered cubic (fcc) and hard body-centered cubic (bcc) phases. The AlCoCrFeNi$_{2.1}$ EHEA, designed using this approach, exhibits an unprecedented combination of high tensile ductility and high fracture strength at room temperature, with excellent mechanical properties maintained up to 700°C. The alloy also demonstrates good castability and is free from compositional segregation, which are common issues in HEAs. The EHEA's microstructure consists of a fine lamellar fcc/B2 structure, with a uniform and fine lamellar microstructure that enables the alloy to achieve a balance between high strength and ductility. The alloy's mechanical properties can be further improved through thermomechanical treatments. Compared to conventional high-temperature alloys like NiAl and NiAl/Cr(Mo) eutectic alloys, the EHEA exhibits significantly higher fracture strength and ductility, as well as a much higher ratio of fracture stress to yield stress. The EHEA's unique combination of properties makes it a promising candidate for high-temperature applications. The study also highlights the potential of using the eutectic alloy concept to design new HEAs, which could lead to the development of more efficient and durable high-temperature materials. The research was supported by the National Science Foundation of China and the Key grant Project of Chinese Ministry of Education. The authors contributed to the design of the experiments, the execution of the experiments, the analysis of the results, and the writing of the paper. The authors declare no competing financial interests.A new class of high-entropy alloys (HEAs), called eutectic high-entropy alloys (EHEAs), has been developed to address the challenges of achieving both high strength and ductility in high-temperature materials. This study introduces a novel strategy using the eutectic alloy concept to design HEAs with a microstructure composed of alternating soft face-centered cubic (fcc) and hard body-centered cubic (bcc) phases. The AlCoCrFeNi$_{2.1}$ EHEA, designed using this approach, exhibits an unprecedented combination of high tensile ductility and high fracture strength at room temperature, with excellent mechanical properties maintained up to 700°C. The alloy also demonstrates good castability and is free from compositional segregation, which are common issues in HEAs. The EHEA's microstructure consists of a fine lamellar fcc/B2 structure, with a uniform and fine lamellar microstructure that enables the alloy to achieve a balance between high strength and ductility. The alloy's mechanical properties can be further improved through thermomechanical treatments. Compared to conventional high-temperature alloys like NiAl and NiAl/Cr(Mo) eutectic alloys, the EHEA exhibits significantly higher fracture strength and ductility, as well as a much higher ratio of fracture stress to yield stress. The EHEA's unique combination of properties makes it a promising candidate for high-temperature applications. The study also highlights the potential of using the eutectic alloy concept to design new HEAs, which could lead to the development of more efficient and durable high-temperature materials. The research was supported by the National Science Foundation of China and the Key grant Project of Chinese Ministry of Education. The authors contributed to the design of the experiments, the execution of the experiments, the analysis of the results, and the writing of the paper. The authors declare no competing financial interests.