Many aerospace structures must operate under combined mechanical and thermal loads. In particular, thin-walled structural members (beams, plates, shells) may carry significant compressive loads while resisting lateral loads in the presence of high and changing temperatures. Structural stability and creep are general concerns under such conditions, especially for polymers and polymer-matrix composites, which have relatively high coefficients of thermal expansion and which may exhibit viscoelastic behavior. The longterm development of structural instability under prolonged high temperature exposure adds potential time-dependent failure modes. The paper describes the application of an internalvariable viscoelastic model to the problem of creep buckling of a simply-supported beam with initial curvature. When the axial compressive load is less than the “rubbery” buckling load (based on the long-time elastic modulus), the response exhibits decaying exponential creep and asymptotically approaches an equilibrium deflected state. When the load exceeds the “glassy” buckling load (based on the short-time modulus), rapid buckling occurs, resisted only by damping and inertia. At intermediate loads, the response grows, eventually resulting in a creep instability. The apparent creep time constant appears to increase with increasing compressive load.