To overcome the limited mechanical properties of single-phase FCC/BCC high entropy alloys, a large effort is being made towards the development of eutectic composites. The eutectic/near eutectic high entropy alloys (EHEAs) with alternate lamellar phases provide an optimum balance between strength and ductility. Therefore, CoCrFeNiNbx (0.45 < x < 0.65) and CoCrFeNiTay (0.2 < y < 0.5) EHEAs comprised of FCC and Fe2Nb/Co2Nb type Laves phase were synthesized by arc-melting and were characterized by x-ray diffraction, scanning electron microscopy and energy dispersive x-ray spectroscopy. Furthermore, a large number of EHEAs comprising of BCC/FCC solid solution phases and intermetallic compound/topologically closed packed (TCP) phases have been surveyed, as reported in the literature. The stability of the phases were assessed by considering the mixing enthalpy (Delta H-mix), valence electron concentration (VEC), and atomic size difference (delta(r)). The eutectic phases in all these EHEAs become stable when -18 <= Delta H-mix <= -6, 6 <= VEC <= 8.5 and delta(r) > 3%. The synergistic effect of Delta H-mix, VEC, and delta(r) on the phase stability and the phase prediction in EHEAs, have been explored. (C) 2019 Elsevier B.V. All rights reserved.