Cold-formed steel structures have been progressively used in structural buildings in the forms of the typical channel and Zed sections. The channel sections under weak-axis bending can be found in various situations, especially under biaxial bending. The flexural capacities about the weak-axis, therefore, have specific impacts on the flexural capacities of the channels. The unsymmetrical feature of this channel section about the weak-axis results in a variety of behaviors and strengths of cold-formed steel channel beams with the change of moment directions. SupaCee -a new form of the channel section -made by adding stiffeners in the web of the channel section to increase the stability of the sectional web is also considered in the investigation. This paper, therefore, is aimed to investigate the behaviors and sectional capacities of the channel and SupaCee sections under the weak-axis bending. The considered sections are taken as the availably commercial sections in the market. The sectional capacities are determined using an innovative method namely the Direct Strength Method as regulated in the Australian/New Zealand Standard AS/NZS 4600:2018. The bending behaviours of the investigated sections are observed and analysed; the obtained strength results are the basis for the evaluation of sectional capacities of the channel and SupaCee sections under variations of moment directions. It was found that capacities of the channel and SupaCee sections under the weak-axis bending can be governed by local or distortional buckling depending on the moment directions, whereas the capacities of distortional failures are higher than those of local failures. Also, the innovative strengths of SupaCee sections under the weak-axis bending are not demonstrated in comparison with these such strengths of channel sections.