Propagation of Pulses in Viscoelastic Media

— It is shown that in hereditary models of media with regular convolution kernels discontinuities propagate with the wavefronts. A singularity always remains sharp and propagates with the wavefront. Oscillatory signals lag behind the wavefronts and are preceded by distortions. In media with singular memory, signals lag behind wavefronts. Singular signals are immediately smoothed and spread out.