The effect of Nb addition in arc‐melted CoCrFeNiNb x (0.45 ≤ x ≤ 0.65) high entropy alloys (HEAs) on the phase evolution, stability, refinement of the microstructure, and mechanical properties are investigated. Minor fluctuation of Nb modifies the microstructure from hypoeutectic ( x = 0.45) to eutectic ( x = 0.5) and hypereutectic ( x = 0.55) containing 134–200 nm thin nano‐lamellar FCC γ ‐Ni and HCP Fe 2 Nb‐type Laves phases. The nano‐eutectic CoCrFeNiNb 0.5 HEA shows high yield strength (2060 ± 5 MPa) and strain hardening up to 2200 ± 10 MPa with 17.0 ± 0.5% compressive plasticity. Transmission electron microscopic studies of partially deformed specimen has been revealed that the activity of dislocations is present in the eutectic FCC/Laves lamellae and at their interface. The stability of the phases in CoCrFeNiNb x and other eutectic HEAs as reported in the literature, has been assessed by estimating mixing entropy (Δ S mix ), mixing enthalpy (Δ H mix ), atomic size differences ( δ ), valence electron concentration, Pauling electronegativity (Δ χ P ), and Allen electronegativity (Δ χ A ) to predict the evolution and coexistence of eutectic phases.