Cold-formed steel (CFS) moment connections are often formed by bolting the webs of the connecting elements to a stiffened gusset plate, and local buckling of the web adjacent to the connection typically governs their capacity. This paper aims to study this failure mode in case the connection is subject to combined axial compression, shear and bending moment. In a first step, the case of pure compressive loading was investigated. Validated GMNIA Finite Element (FE) models were used to investigate the effects of different design variables, including the cross-sectional geometry and thickness, the bolt group configuration and the bolt group length. The results were then used to develop design equations for the compressive capacity of CFS bolted connections. In a next step, the FE models were used to assess the capacity of CFS bolted connections subject to combined bending and shear, and combined axial compression, bending and shear. Suitable interaction equations were proposed and reliability analyses were performed within the framework of both the Eurocode and the AISI standards. It was concluded that a linear equation accurately captures the interaction between bending moment and axial force, while the effects of a shear force smaller than half of the shear capacity on the bending moment capacity can be neglected