A general formalism is derived, that allows the evaluation of magnetic instabilities of all types of electric arc. It is shown that a stability criterion exists which is determined by the interaction between the magnetic forces, the frictional force and the so-called isotherm movement. This criterion can be expressed in terms of a dimensionless parameter Mk: when Mk is smaller than a critical value Mk cr , then the arc is absolutely stable, when Mk = Mk cr a stationary, deflected condition arises, and when Mk>Mk cr the arc is unstable. Depending on the magnitude of the growth rate however, a convective stabilisation, caused by an axial flow component, can result. The results of the theory are applied to a variety of technically interesting arcs, such as axially blown arcs, arcs in gaps and transversely blown arcs.