Discrete auroral arcs appear as bright structures along geomagnetic field lines, and they are associated with precipitating electrons and field-aligned currents. Because of the magnetic shear produced by these field-aligned currents, such configurations may be unstable with respect to the tearing mode instability. We suggest that the tearing instability and magnetic reconnection may cause the small-scale filamentation of auroral arcs as it is observed in auroral spirals and folds. We derive a dispersion relation for the resistive tearing mode for systems with a neutral gas background which is present in the ionosphere. The dispersion relation provides onset criteria for the instability due to the strong damping of the mode for parameter regimes that involve a strong coupling of the plasma and the neutral gas component. For reasonable ionospheric parameters we solved the dispersion relation numerically. The growth time of the mode (approximately a few minutes) and the resulting spatial structures are in accordance with typical values observed for spirals and folds. By employing a new quasi-neutral three-fluid code, we carried out several runs in order to test the linear theory. The results confirm the linear theory for the considered fluid parameters and illustrate the evolution of a possible reconnection processes within arclike configurations where the plasma-neutral gas interaction due to frictional forces is taken into account. ¿ American Geophysical Union 1992