We devise a model to investigate the interplay between two common phenomena affecting the evolution of a seismogenic fault: the occurrence of earthquakes on neighbouring faults and the partial degree of anelasticity of rocks in the upper mantle, a feature that is often manifested by a post-seismic process known as viscoelastic relaxation. We show how this process dramatically complicates the way an earthquake may alter the magnitude and timing of a seismic event on the perturbed fault.