We present a method for early detection of runaway initiation in batch and semibatch isoperibolic reactors using only temperature measurements, and based on the calculation of the divergence of the system by applying state space reconstruction techniques. The method is illustrated for simulated as well as experimental data sets. The results show that the algorithm is able to distinguish between runaway and non-runaway situations and it does not produce false alarms even during semibatch dosed-controlled experiments. For the case of the experimental data sets, due to fluctuations and noise present in the measurements, it is necessary to apply non-linear filters to improve the performance in terms of early detection and number of false alarms. Finally, we show that the divergence is a generalisation of former criteria for on-line detection. (C) 2003 Elsevier Ltd. All rights reserved.