Body‐centered cubic refractory high entropy alloys (RHEA) are promising for high‐temperature structural application due to their exceptional properties, particularly in terms of yield strength at elevated temperatures. For certain alloy systems, such as Mo‐Ti‐Cr‐Al, both disordered (A2) and ordered (B2) crystal structures are possible. In this particular system, a solid‐state transformation from A2 to B2 during cooling occurs. For Al concentrations above approximately 10 at.%, B2 order is obtained from the transformation temperature down to room temperature, while A2 is stable above room temperature below the critical Al content. In this study, two alloys from the Mo‐Ti‐Cr‐Al system close to the transition between A2 and B2 were investigated. Nanoindentation tests revealed that the magnitude of strain rate sensitivity for both alloys is small compared to classical alloys, however, significantly temperature dependent up to the strength plateau temperatures. The yield strength plateau, which is insensitive to the strain rate, was observed at temperatures exceeding 573 K. Modelling of solid solution strengthening reproduces the experimental data in the Al‐lean A2 alloys. However, the observed discontinuous increase of strength in the Al‐rich B2 alloys can only be rationalized by the appearance of B2 order and to no significant other obvious strengthening mechanisms.This article is protected by copyright. All rights reserved.