Naturally buckling steel braces (NBBs) have been recently developed by the authors and co-workers to improve the buckling performance and energy dissipation capacity of braced framed structures. In NBBs, a low-yield-point steel (LYS) channel and a high-strength steel (HSS) channel are connected using steel battens to build up a dualmaterial steel section. An intentional eccentricity is introduced along the brace length to subject the brace to bending loads in addition to axial loads. Previous experiments have demonstrated that this combined axialflexural response stabilizes the compression behaviour of the brace and enhances its tensile post-yielding stiffness through a novel deformation mechanism. In this paper, the cyclic behaviour of two full-scale NBB specimens with different section sizes and eccentricities are investigated experimentally. Gusset plate pin-connections that accommodate in-plane buckling are used to release the brace ends from high ductility demands. Two low-cycle fatigue protocols with increasing amplitudes and repeated inelastic loading cycles at the event of local buckling are adopted. Test results show that both NBB specimens exhibited a stable hysteresis behaviour by delaying the onset of local buckling up to a 1.5 % story drift ratio (SDR). Notably, the specimen with larger section and larger eccentricity provided a stable tensile strength under five repeated loading cycles of 2.0 % SDR. An equivalent damping ratio of 0.4 was measured. In addition to the experimental research, a computational study is performed with the aid of the finite element software ABAQUS to evaluate partially strengthening method of the sections against local buckling. It was found that the energy dissipation capacity of NBBs can be enhanced up to 40% by using rib stiffeners at critical locations, while the use of thicker channel battens can provide further restrain to local buckling growth up to a 3.0% SDR. The paper develops the physical equations to support an analytical hysteretic model for predicting the force-displacement cyclic relationship of chevron NBBs. The accuracy and targeted conservatism of the proposed hysteretic model is confirmed through comparisons with the test results.