Аннотация:Kirchgässner reduction was used to treat convection in a plane layer between insulating boundaries. In this formulation a one parameter family of equilibria exists with the stability spectrum depending on a point on it. This phenomenon is similar to the one observed in problems with cosymmetry since on a center manifold in the vicinity of a line of equilibria nontrivial cosymmetry exists. It is demonstrated that on a spatial center manifold in the vicinity of a line of equilibria, the bifurcation picture depends on the choice of the boundary conditions which leads to different reversible problems.