A unified approach that relates and combines the concepts of parametric sensitivity, ignition, extinction, hysteresis and isola formation is presented and used to derive a single universal runaway criterion valid for all homogeneous reactor models. It is also shown that the heat and mass dispersion have very little impact on this runaway locus. Next, the approach is extended to heterogeneous reactor models where interphase gradients strongly influence the runaway boundary. It is shown that the model of a well-mixed two-phase reactor may be used to derive runaway boundaries for a cooled multitubular catalytic reactor influenced by interparticle and intraparticle transport limitations. The validity of the approach is verified by numerical simulations of temperature profiles under safe and runaway conditions for some selected cases. The analysis of the heterogeneous model shows that the heat transfer resistance between the solid and the fluid introduces a qualitative change in the shape of the stability boundary. There exists a limiting value of the dimensionless heat of reaction parameter B, above which the reactor is in a runaway region regardless of the rate of external cooling. This limiting value of B corresponds to the ignition of catalyst particles. It is also shown that within the safe region of operation, there exists an optimal catalyst particle diameter that maximizes the reactor productivity. The main concepts involved and computation of the runaway boundaries for multiple reactions are illustrated by discussing three specific examples of consecutive, simultaneous and consecutive-simultaneous reactions. The important result is that the runaway locus for any multiple reaction network differs significantly from that of the single reaction only when the product lambda(b)psi > 0.1. Here, lambda, psi and b, represent, respectively, the ratio of rate constants at feed conditions, heats of reaction and feed concentrations of the primary reaction to that of the main competing reaction. This work also presents slightly conservative analytical results for the determination of the runaway limits of homogeneous and catalytic reactor for most cases of practical interest.