Concentrically braced frames are a common form of earthquake resistant structure. Performance of the structure is largely dependent on the ability of the key dissipative components, in this case the diagonal bracing members, to undergo significant inelastic deformations. Whilst many earlier studies have examined the hysteretic response of bracing members, comparatively less attention has been given to the ultimate behaviour and failure conditions. There are also significant uncertainties in existing models for predicting the ductility capacity of braces owing to their semi-empirical nature as well as the scatter of test results. This research project examines the cyclic behaviour of tubular braces made of a familiar structural material, carbon steel, and an increasing popular alternative structural material, stainless steel, which is known for its high tensile ductility. As part of the current study, laboratory tests were performed on hot-rolled carbon steel, cold-formed carbon steel and cold-formed austenitic stainless steel hollow section members and materials coupon cut from them. A total of 24 tensile coupon tests, 62 cyclic material tests and 16 cyclic member tests were conducted. Strain-life relationships of the materials under low and extremely low cycle fatigue regimes were established from the results of the cyclic material tests. These data were also used for calibrating material cyclic hardening models, which were incorporated in numerical models of hollow section members. These models, verified against the results of the cyclic member tests from this study and other research programmes, were employed in parametric studies to investigate the influence of member geometry and material properties on the behaviour of the bracing members. Although the three materials exhibit similar strain-life relationships, cold-formed stainless steel members perform better in terms of displacement ductility and energy dissipation, which is due to the cyclic hardening and higher post-yield stiffness of the stainless steel material. Implications of these findings on the design of earthquake resistant concentrically braced frames are discussed and design guidance for stainless steel bracing members is proposed.