DEMETER (Detection of Electro-Magnetic Emissions Transmitted from Earthquake Regions) is an ionospheric microsatellite launched on a polar orbit at an altitude of 710 km. Its scientific payload allows to measure electromagnetic waves and plasma parameters. During the strong magnetic storm from 8 to 10 November 2004, intense electromagnetic harmonic emissions between 500 and 2000 Hz have been detected at midlatitudes and similar emissions were also observed on 21--22 January 2005 and on 15 May 2005 during two magnetic storms of lower intensity. They can be observed on consecutive orbits, either in one hemisphere or in both hemispheres at the same L values. On the dynamic energy/time spectrograms that are available in the DEMETER survey modes these emissions appear most often as patches of intensified signals lasting a few tens to hundreds of seconds with a frequency structure showing nearly equally spaced frequency bands. Such a frequency structure could be explained if the waves originate from the generation of Electro-Magnetic Ion Cyclotron (EMIC) waves at proton cyclotron harmonics. When waveforms are available during burst modes, allowing a fine-resolution frequency analysis, these emissions appear in one orbit be composed of a set of lines slowly drifting in frequency with time. During periods with a high magnetically activity, the ionosphere and the magnetosphere are severely disturbed and these waves could be generated at relatively low L values and propagate from their equatorial source region along density gradients down to the altitude of the satellite. Energetic electron data obtained onboard DEMETER indicate that these waves interact with the energetic electron populations.