A good comprehension of the uniaxial ratchetting behaviour is an effective method to improve the reliability and the durability of 2024 Aluminium alloy components during in-service loading conditions. For this purpose, experimental fatigue tests have been performed under stress range control. The maximum axial deformation proved to have an atypical oscillatory evolution which in turn has a doubly oscillatory form. This behaviour was found to experience two scenarios consisting of a succession of hardening and softening blocs. The interpretation of this behaviour, which found its origin at the microscopic scale, was in good agreement with previous experimental works performed under cyclic TC and TT90 loadings in strain-controlled mode. Indeed, it was assumed that this behaviour is attributed to dynamic strain ageing (DSA) due to the repeated locking and unlocking of dislocations by the diffusive solute atoms and precipitates during cyclic loadings.