The stability of toroidicity‐induced drift waves in a tokamak equilibrium with magnetic separatrix is studied both analytically and numerically. In particular, the task of a proper determination of the complex ballooning parameter &thgr;0is performed by solving the stationarity condition for the eigenvalue. Results show qualitative dependence on the location of the x point in the meridian plane. Specifically, locating the x point in the equatorial plane, both on the outside and on the inside of the plasma, causes a deepening of the well structure in the potential for the eigenmode, thereby enforcing the inhibition of the shear damping and the marginal stability result obtained in the circular magnetic surfaces case. On the other hand, the location of the x point at the top of the plasma produces a flattening of the well and restores the shear damping, yielding stabilization of the mode. A new quasimarginally stable branch, corresponding to modes localized around the x point, is shown to exist at high values of the separatrix parameterkand x‐point location close to the equatorial plane.