This two-part article gives an overview of the developments of the structural member verification in prEN 1993-1-1:2020 “Eurocode 3: Design of steel structures - part 1-1: General rules and rules for buildings”, one of the second generation of Eurocodes. These developments were undertaken by Working Group 1 (WG1) of Subcommittee CEN/TC250/SC3 and by Project Team 1 (SC3.PT1) responsible for drafting the new version of EN 1993-1-1. In the past, WG1 collected many topics needing improvement, and the systematic review conducted every five years also yielded topics needing further development. Based on this, the current version of EN 1993-1-1 has been developed into a new draft version prEN 1993-1-1:2020 enhancing “ease of use”. The technical content of this new draft was laid down at the end of 2019. Many improvements to design rules have been established with respect to structural analysis, resistance of cross-sections and stability of members. This two-part article focuses on member stability design rules and deals with the basis for the calibration of partial factors, the introduction of more economic design rules for semi-compact sections, methods for structural analysis in relation to the appropriate member stability design rules, new design rules for lateral torsional buckling plus other developments and innovations. This second part of the article is dedicated to illustrating the most relevant changes to member buckling design rules.