The determination of critical conditions for thermal ignition of combustible materials has been traditionally studied by the use of one overall reaction with bounded parameter values for the activation energy and other chemical constants, Significant errors can occur in the values of the threshold parameters for ignition when there are two (or more) simultaneous reactions present with distinct values of the chemical constants. Recent work with simultaneous parallel reactions showed the thresholds for ignition could be lowered in this case. In this paper, motivated by experimental results for forest litter and coal, it is shown that for sequential reactions (different values of parameters in different temperature ranges) that the threshold conditions are changed (safer for lower ambient temperatures and less safe for higher ambient temperatures).The mathematical analysis is summarised and a detailed analysis is given for the forest litter and crushed coal applications. The experimental results show that variable activation energy does occur and that this extension of the classical Frank-Kamenetskii theory is needed. Here the analysis is confined to the slab geometry only but the ideas developed can easily be extended to more general systems, including those involving mass transport, consumption, and phase changes. The determination of critical conditions for thermal ignition of combustible materials has been traditionally studied by the use of one overall reaction with bounded parameter values ​​for the activation energy and other chemical constants, Significant errors can occur in the values ​​of the threshold parameters for ignition when there are two (or more) simultaneous reactions present with distinct values ​​of the chemical constants. Recent work with simultaneous parallel reactions showed the thresholds for ignition could be lowered in this case. In this paper, motivated by experimental results for forest litter and coal, it is shown that for sequential reactions (different values ​​of parameters in different temperature ranges) that the threshold conditions are changed (safer for lower ambient temperatures and less safe for higher ambient temperatures). The mathematical analysis is summarised and a detailed analysis is given for the forest litter and crushed coal applications. The experimental results show that variable activation energy does occur and that this extension of the classical Frank-Kamenetskii theory is needed. Here the analysis is confined to the slab geometry only but the ideas developed can easily be extended to more general systems, including those involving mass transport , consumption, and phase changes.