We consider the mode-interaction [1, 2] between a steady-state bifurcation and Hopf bifurcation in a system with O(2) symmetry. It is somehow a natural configuration that emerges in many fluids of interest: Taylor-Couette flow (TCF), the wake flow [7, 6, 8, 4] of axisymmetric objects (WFA) and the wake of axisymmetric objects in mixed convection (WFA-MC). In here we analyse the bifurcation scenario of the WFA-MC problem for two axisymmetric bodies, a disk with variable thickness and the sphere. Other axisymmetric problems have been also recently explored, such as the hope past a circular aperture [3, 5] In these cases, the flow state q = [u, p] composed of the velocity field and the hydrodynamic pressure (the WFA-MC also includes the temperature field T) is decomposed as: q = Q 0 + Re a 0 (t)e −iθ ûs + Re a 1 (t)e −iθ ûh,−1 + a 2 (t)e iθ ûh,1 (1)