The stability limit to the under-excited operation of synchronous generators is expressed in terms of two-axis reactances. These reactances have in the past generally been those applicable for rated load or corresponding with the short-circuit ratio. Modern large solid-rotor generators are heavily saturated and the use of these fixed reactances introduces error. Reactances appropriate to limiting operation are obtained here together with their derivatives with respect to load angle to give the limit. New limits for two large machines are presented. The new limits are more restrictive than when rated-load reactances are used but less restrictive than using those associated with the short-circuit ratio.