The definition and determination of the critical conditions for thermal ignition in materials which are undergoing an exothermic reaction are described, using the steady-state theory, for a wide class of reactions. The equations discussed are those for a steady-state thermal regime with non-linear (with temperature) heat generation in the material with a linearized radiation condition on the boundary. Reactant consumption is ignored. It is shown that the character of the spectrum of the corresponding non-linear eigenvalue problem depends crucially on the form of the non-linearity, which is usually taken, in real situations, as the Arrhenius function, or an approximation to it. The point at which there is a discontinuity (or bifurcation or jump), in the minimal stationary thermal regime is defined as the critical condition. It is shown that this value can be determined by a variational method, which is minimax in character. The value of the critical parameter, defined in this way, is shown to approach the critical value as defined by Frank-Kamenetskii (for simple geometries) continuously from above, as the activation energy tends to infinity, when the Arrhenius function is approximated by an exponential one. Further, it is shown that the occurrence of critical behaviour can disappear for sufficiently low activation energies. For very high activation energies, the thermal regime is shown to approach that of a Semenov regime with uniform temperature.