Theoretical considerations and previous experimental findings with fast tubular (cylindrical sheet) pinch discharges are reviewed briefly. More recent work with magnetic probes, as well as streak and Kerr cell photography, corroborates that the sheet‐current configuration can be sufficiently stable to survive a fair number of pinch oscillations. It is shown, however, that under conditions of high compression the current layer is likely to break up into a set of individual channels because of a resistive instability. The process involves tearing and reconnection of magnetic field lines. Wavelengths and growth rates seem to be in agreement with rough theoretical predictions. The current channels form separate linear pinches, which under certain circumstances disintegrate subsequently by a secondary instability. A generally turbulent behavior results. Tearing is not prevented by superposition of a strong axial magnetic field, again in agreement with theory, although a slight retardation is noted. When deuterium is used in the discharge, neutrons are emitted. Presumably because of the slow rate of reconnection in most of our studies, the neutrons appear mainly during the secondary instability, rather than at the time of tearing. These findings are of interest both to astrophysics and to controlled‐fusion research.