Temperature and concentration evolution in a spatially homogeneous reacting system is described by a dynamical system characterized by a vector field accounting for reaction rates and heat exchange with the surroundings in a lumped way. This article addresses the estimate of the explosion limits and the assessment of runaway criteria in batch reacting systems by focusing on the evolution of the stretching rates along system trajectories. The stretching-based runaway criteria are applied in archetypal systems, such as the Semenov model, and compared with classical sensitivity-based criteria and with other detection methods derived from dynamical system theory. Several other examples are thoroughly addressed, including an isothermal combustion model (the chain-branching model) and the explosion limits in the H-2-O-2 system. (c) 2006 Elsevier Ltd. All rights reserved.