This work presents first results and the numerical methods of a highly improved two-dimensional three-fluid simulation model of the ionosphere-magnetosphere system. The model considers ionization and recombination, ion-neutral friction, the Hall term in Ohm's law, and various heat sources in the energy equations. The electrodynamic response and the evolution of the collision frequencies are treated self-consistently in the height-resolved ionosphere. This model is the first and to our knowledge the only simulation model that can resolve the dynamic and nonlinear electromagnetic interaction between the ionosphere and the magnetosphere. The simulation is aimed at modeling fast temporal and small spatial scale ionospheric structures associated, for instance, with filamentary aurora and ionospheric heating experiments. The results presented in this paper focus on ion and electron heating by different sources, i.e., ion heating due to plasma-neutral friction, electron heating resulting from energetic particle precipitation and by ohmic dissipation in strong field-aligned currents. This work is motivated by a specific auroral event that was observed simultaneously with optical and radar instruments. A consistent explanation of this event is possible in the presence of ohmic heating of electrons in a strong field-aligned electric current layer. ¿ 2001 American Geophysical Union