Expansion techniques are used to obtain analytic expressions for the stability criterion of toroidal hydromagnetic equilibria with l = 2 or l = 3 multipolar fields. The first case shows that care must be taken in using stability criteria in which the coupling of the Fourier modes of the perturbation is not correctly treated. The latter demonstrates the restrictions which the equilibrium criteria can impose on the system if the rotational transform vanishes somewhere in the system.