In the present investigation, the nonlinear static as well as dynamic buckling of asymmetrical suspended roofs, acted upon by step conservative loading of infinite duration is examined in detail. This is achieved via a two-degrees-of-freedom imperfect dissipative model simulating the real roof structure. Natural and complementary equilibrium paths are determined for different characteristic values of the parameters involved, revealing a variety of equilibrium configurations. Evolution from symmetry to asymmetry, especially for high roofs, changes the static response from limit point instability to monotonically rising stable paths and increases the amplitude of horizontal displacement. For all cases considered the corresponding dynamic response is associated with point attractors, being either remote stable physical equilibria or prebuckling fixed points, simultaneously locally and globally asymptotically stable, although the dynamic buckling phenomenon has already occurred. The main feature of suspended roofs - sensitivity to horizontal vibrations - is captured by the proposed model, while eliminating the effect of suspension the model yields snap-through buckling as expected.