The current pulses delivered through platinum electrodes by medical implants to recruit neurons give rise to slowly decaying voltage tails, called "artefacts." These tails make measurement of evoked potentials following the pulses very difficult. We present an evidence to show that in a typical clinical scenario, these tails are mostly caused by the concentration gradients of species induced in the electrical double layer adsorbed onto the surface of both stimulating and passive electrodes. A compact model is presented that allows the simulation of these artefacts. The model is verified against measurements made in saline. This shows that electrode artefacts are an intrinsic property of the conductive electrodes of a lead.