Fig. \[fig3\].

![Resistance vs current hysteresis loop (after Grollier [*et al.*]{} [@16]). []{data-label="fig3"}](Fig3.eps){width="8cm"}

It can be seen from Fig. \[fig3\] that, for any given current, the switching magnet moment is stationary (the junction resistance has a well defined value), [*i.e.*]{} the system is in a steady state. This holds everywhere on the hysteresis loop except for the two discontinuities where current-induced switching occurs. As indicated by the arrows jumps from the parallel (P) to anti-parallel (AP) configurations of the magnetisation, and from AP to P configurations, occur at different currents. It follows that in order to interpret experiments which exhibit such hysteresis behaviour, the first task of the theory is to determine from the LLG equation all the possible states and then investigate their dynamical stability. At the point of instability the system seeks out a new steady state, [*i.e.*]{} a discontinuous transition to a new steady state with the switched magnetisation occurs. We have tacitly assumed that there is always a steady state available for the system to jump to. There is now experimental evidence that this is not always the case. In the absence of any stable steady state the switching magnet moment remains permanently in the time-dependent 