The paper 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 × ≥ 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 × ≤ 0.2 surprisingly the opposite effect is observed. As in case of the undeformed CoCrFeMnNiVx alloys, the behaviour for vanadium concentrations × ≥ 0.5 can be related to the formation of tetragonal σ‐phase in addition to fcc matrix, while the anomalous behaviour for × ≤ 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 HEAs ‐ 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 non‐thermal inertial dislocation movement.This article is protected by copyright. All rights reserved.