The instability of beam-columns with crossarms and externally prestressed cable stays is studied analytically, where the combination of bending and compression is assumed to be derived from the system self-weight acting orthogonally to the applied axial load. A nonlinear analytical model for prestressed stayed beam-columns with doubly-symmetric and mono-symmetric configurations, based on the Rayleigh–Ritz method, is presented that captures modal interactions for perfect geometries explicitly for the first time. It is demonstrated that the theoretical compressive strength enhancements under certain configurations can only be obtained at the expense of triggering a sequence of destabilizing bifurcations. This can give rise to severely unstable interactive post-buckling behaviour including the so-called ‘mode jumping’ phenomenon. Moreover, for mono-symmetric stayed beam-columns, it is shown that the varying levels of prestress within the stays can lead to different buckling modes which all have their own characteristic post-buckling responses. The analytical model is verified using a nonlinear finite element model formulated within the commercial code ABAQUS and excellent comparisons are obtained.