A set of instabilities which are fastest in the weakly collisional regime, being slowed down by increasing electron‐ion collisions, is presented. They take place in configurations having very low pressures, sheared magnetic field, and current flowing along it. These instabilities are driven by the transverse gradient of the longitudinal current, are connected with the effects of electron inertia, and characterized by two types of mode. Modes of one type are electrostatic and localized, having eddies of relatively short scale length, and exist for small and finite wavelengths. The other modes are nonelectrostatic, nonlocalized, and result from one which is singular in the hydromagnetic limit. These exist only for wavelengths of the order of the width of the plasma column, in which limit they are faster than the electrostatic type of modes. The relationship between these instabilities and the known ``tearing'' resistive mode is studied. The growth rate of this is, in fact, increased by ion‐electron collisions and corresponds to transfer of magnetic energy into plasma kinetic energy by decoupling the motion of particles and lines of force. A brief discussion of experimental results offering indication for the modes discussed above is finally given.