Stability of doublet plasmas in the Doublet III device against resistive axisymmetric MHD modes has been studied. The real characteristics of the device were modelled as accurately as possible. Thus, for example, the actual toroidal geometry was used, the field shaping coils (F-coils) which surround the plasma were included, and the location of real limiters was incorporated for determination of the plasma surface. We have used two parameters to model the plasma current distribution and the equilibrium boundary conditions: one describes the flatness of the current profile, the other describes the fraction of the poloidal plasma flux contained within the separatrix. Thus we have determined stability as a function of these two parameters. If the fluxes at the F-coils are kept fixed, there are stable as well as unstable regimes in this two-dimensional parameter space. If the F-coil fluxes are controlled to imitate the presence of virtual F-coils with fixed fluxes located closer to the plasma, it is possible to stabilize the plasma. This stabilization is discussed in the paper and numerical examples are given. Finally, the relationship between the results of this paper and experimental observations from Doublet III is discussed.