This paper is concerned with the cubic autocatalator, A + 2B→2B, B→C, in a closed system, in particular when the extra uncatalysed reaction A→B, the quadratic autocatalytic reaction A + B→2B and the additional decay step A→C are included. Previous work has shown that the oscillatory behaviour in the original scheme is structurally unstable with respect to the inclusion of the uncatalysed reaction. Here the equations exhibit a more complex pattern of behaviour than was present in previous studies and this has been fully investigated using constructional methods developed by Gray and Roberts. It is shown that the basic scheme is also structurally unstable with respect to the inclusion of the quadratic autocatalytic step. However, the inclusion of the extra decay step A→C has the effect of removing this structural instability by bringing into the finite phase plane behaviour that was previously seen at infinity.