A general class of self‐similar, time dependent, non‐stationary z‐pinch equilibria is examined in detail It is shown that there are several zones of parameter space, corresponding to various types of solution. One‐dimensional simulations reveal that the self‐similar solutions act as attractors. The instaneous linear MHD growth rates for them=0andm=1instabilities are found to be almost the same for all the solutions. Thus there is no especially favourable subset of the equilibria to aim for experimentally.