The author studies Delta '-driven resistive ballooning modes in a model equilibrium which has a separatrix. The author illustrates the effect of the separatrix on these modes by considering the variation of Delta ' as a function of a pressure gradient parameter, alpha , for various flux surfaces, ranging in shape from circular to one which has an X-point. The author finds that inclusion of the resistivity increases the region of instability of the plasma to ballooning modes.