The article presents investigations of microstructure and low‐temperature mechanical properties of nanostructured alloys CoCrFeMnNiVx (x = 0.15–0.75), processed by high‐pressure torsion (HPT) at temperatures of 300 and 77 K. While at x ≥ 0.5 the values of microhardness (Hv) and compression yield stress (σ0.2) in samples after HPT at 77 K are larger than those in samples after HPT at 300 K, for x ≤ 0.2 surprisingly the opposite effect is observed. As in case of the undeformed CoCrFeMnNiVx alloys, the behavior for vanadium concentrations x ≥ 0.5 can be related to the formation of tetragonal σ‐phase in addition to face‐centered cubic matrix, while the anomalous behavior for x ≤ 0.2 arises from the formation of HPT‐induced hexagonal martensitic phase. In the low‐temperature ranges, i.e., 20–300 K in case of HPT nanostructured CoCrFeMnNiV0.2, and 150–300 K in case of HPT nanostructured CoCrFeMnNiV0.5, dependences of σ0.2(T) show characteristics of thermally activated dislocation movement. For the first time in high‐entropy alloys, anomalous dependences of σ0.2(T) at temperatures 4.2–20 K for CoCrFeMnNiV0.2, and at 80–150 K for CoCrFeMnNiV0.5 are found, which indicate at the occurrence of nonthermal inertial dislocation movement.