Using plasma wave data sampled by the Freja spacecraft from the topside ionosphere during auroral conditions, the possible existence of electric fields with an intense parallel component (a few tens of millivolts per meter) with respect to the Earth's magnetic field is discussed. When Freja crosses large-amplitude solitary electromagnetic structures (ΔE≈100 mV/m and ΔB≈10 nT, identified as being solitary kinetic Alfv¿n waves), strong electric spikes are sometimes detected along a direction almost parallel to the static magnetic field. The possible sources of errors due to the plasma inhomogeneities and/or to the magnetic connection between the electric probe and the spacecraft body are reviewed and discussed. In particular, using an indirect technique based on the reconstruction of the electric field hodograms, it is shown that these sources of errors have no influence on our conclusions. Unless unknown mechanisms strongly affect the validity of double-probe measurements in some circumstances, it is then concluded that an electric field with a parallel component 2--3 orders of magnitude larger than expected from the theory of kinetic Alfv¿n waves can develop in the topside ionosphere. ¿ 1998 American Geophysical Union