We study the large time behavior in L2 of solutions to a model for the motion of an unbounded, homogeneous, viscoelastic bar with fading memory. Decay rates for the solutions are obtained under the assumption that the initial data and histories are smooth and small. Moreover, convergence of the solutions to diffusion waves, which are solutions of Burgers equations, is proved and rates are obtained. Our method is based on the study of properties of the solutions to the linearized system in the Fourier space. © 1992 Springer-Verlag.