The author obtains a general criterion for the stability of a toroidal plasma with respect to g-mode perturbations, which were first considered by Furth, Killeen and Rosenbluth for a plasma of finite conductivity in a magnetic field with shear and gravitational field g. The criterion is used to elucidate the stability of g-mode perturbations in an axially symmetric tokamak of circular cross-section. It is shown that, if aq'/q is positive and not too small, g-mode perturbations are stable for q2 > 1 (where q is the safety factor, a is the radius and the prime denotes a derivative with respect to a). With negative values of aq'/q, instability is possible even if q2 ≫ 1.