<p>Electrophoresis, a crucial technique in medical diagnostics, enables the control of individual particles, molecules, viruses, and bacteria during single-cell analysis. Ion-selective outer layers are often present in many viruses and bacteria. Theoretical and experimental studies on ion-selective granule electrophoresis reveal the existence of various nonlinear modes influenced by the strength of the electric field. Concentration polarization near such granules can lead to instability and chaotic behavior in sufficiently strong electric fields. While most research focuses on electrophoresis in Newtonian fluids, it is well-known that biological fluids exhibit non-Newtonian properties due to the presence of polymer molecules. This paper presents numerical simulations of electrophoresis in viscoelastic electrolytes modeled as Oldroyd-B and FENE-CR fluids. Microscale statement is considered, so gravitational and other inertial effects are neglected. For the electrophoresis of the first kind, we obtained the dependence of the granule’s electrophoretic velocity on polymer concentration and relaxation time. For the electrophoresis of the second kind, we found that the velocity can either increase or decrease with increasing polymer concentration, depending on the Weissenberg number. The presence of polymers led to the emergence of unsteady electrophoresis regimes caused by electrokinetic instability and concentration trace instability. The critical electric field strength values, indicating the onset of non-stationary electrophoresis modes when exceeded, were obtained.</p>