The stochastic stability of a single degree-of-freedom (SDOF) nonlinear viscoelastic system under the excitation of wide-band noise is studied in this paper. An example of such a system is the transverse vibration of a viscoelastic column under the excitation of stochastic axial compressive load. The equation of motion is an integro-differential equation with parametric excitation. The stochastic averaging method and averaging method for integro-differential equations are applied to reduce the system. The largest Lyapunov exponents and stochastic bifurcation are studied after the averaged sytem is obtained.

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