In this paper we investigate the behaviour of higher order Galerkin expansions of the Moore-Greitzer model of general transients in aeroengine compression systems. We assume steady state entrainment of the higher Fourier modes of the rotating stall cell which helps establish a framework for a simplified numerical analysis of the bifurcating solutions corresponding to rotating stall. For small values of the Greitzer surge parameter (B) we discuss general trends in the character of the pure stall solutions. The rotating stall characteristic is shown to exhibit deep hysteresis with a cubic compressor characteristic, establishing the fact that deep hysteresis to a certain extent is a multi-mode phenomena. Elimination of the hysteresis associated with the bifurcation into stall is accomplished in simulations with a combined feedback on the displacement from the peak of the compressor characteristic and the magnitude of the first mode amplitude of the stall cell. Behaviour for larger values of the B parameter is also investigated and novel surge/stall relaxation oscillations corresponding to classic surge are discovered.