The stability requirements of in-core thermionic reactor concepts are examined analytically, utilizing an approximate two-region description of the fueled diode. General stability requirements for the model are derived and then evaluated for possible ranges of design considerations with regard to operating power-density levels, diode dimensions and materials, and fuel materials. The stability of this type of reactor is shown to be only weakly dependent on design considerations provided the static power coefficient is negative. The reactor is sluggish in its response to reactivity or load perturbations, the response time to reattain equilibrium being of the order of minutes. A comparison between the approximate stability criterion and the corresponding criterion obtained from a detailed analog-computer simulation of a specific reactor concept indicates the approximate criterion is conservative, as postulated.