The present study is focused on the local stability of concrete-filled and partially-encased stainless steel sections, fabricated from duplex and lean duplex plates, under axial compression. A total of 34 specimens with box, circular, and I-shaped sections are investigated. Geometrical imperfections of the fabricated stainless steel specimens are measured prior to testing. Following the experiments, a comprehensive parametric study is conducted using finite element method. Results of the experiments as well as the parametric study are then synthesised to recommend axial slenderness limits for the investigated section types. The recommended limits are compared with those stipulated by current design specifications for carbon steel-concrete composite sections. The findings are also compared with the previous data available in the literature for austenitic composite sections and the similarities and differences are highlighted and discussed. The experimental and numerical results are further investigated to calibrate effective width relations to exploit the post-local buckling reserve strength of the studied sections. To facilitate the comparison of the findings with current codified requirements and other studies, the recommendations are presented in three notations used typically by the Australian, American, and European standards.