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For a simple single-zone building on fire with two openings and opposing wind, a theoretical analysis of smoke flow rate and smoke flow direction is carried out. With the same setting of building geometry and physical conditions at steady state, three solutions of smoke flows are identified. Fundamental concepts of nonlinear dynamics are used to show that two of these solutions are stable. One stable solution allows the establishment of the two-layer flow pattern with an upward smoke flow, which may be considered relatively safe in terms of control of smoke flows. The other stable solution is a potentially unsafe situation of downward smoke flow pattern with smoke filling the entire building. We believe that existence of solution multiplicity of smoke flows in this simple building demonstrates that a further study of more complex and realistic situations is necessary.