Electrophoretic motion is analyzed for a neutrally buoyant, non-Brownian prolate spheroid suspended in an electro-osmotic flow developed in a flat microelectrophoresis cell. Neglecting the double-layer deformation, the trajectory and orientation of the spheroid is computed to assess the significance of particle motion in a lateral direction during an electrophoresis experiment. The double-layer thickness of the spheroid is arbitrary. In a closed microelectrophoresis system the electro-osmosis results in a parabolic flow field. During a short period of time (several seconds) the spheroid may deviate significantly in a lateral direction from a straight path parallel to the applied electric field. During a longer period of time (several minutes) the spheroid undergoes a sinuous motion in which it translates periodically back and forth across a straight path along the main flow direction. The spheroid may also translate along a closed trajectory. In all cases the orientation of the spheroid follows the equation for Jeffery orbit.