Aims: To mathematically model published thermal inactivation data sets using an empirical model based on a double Arrhenius function. Methods and Results: A mathematical model, the log R -fa (t) , provided an excellent description of the data sets available: the thermal inactivation of Salmonella anatum at 55degreesC, Pseudomonas viscosa at 48degreesC and Streptococcus faecalis at 60degreesC; Clostridium botulinum spores at various temperatures in the range of 101-121degreesC (two data sets); thermal inactivation of Salmonella Bedford over the temperature range 50-58degreesC, water activity range of 0.94-0.99 and a pH range of 4-7; Bacillus stearothermophilus spores from 105 to 121degreesC and the dry heat sterilization of an indigenous mesophilic soil population over the temperature range of 120-160degreesC. Conclusions: The log R -fa (t) model, derived from previously published chemical inactivation studies provides as good, if not better, description of thermal inactivation kinetics as other published models. The model does not invoke either of the two hypotheses of inactivation: the mechanistic or vitalistic, although it is closely linked to descriptions of the former. Significance and Impact of the study: The log R -fa (t) double Arrhenius function provides the investigator with a relatively simple and easy mathematical model to apply to data of thermal inactivation. This model may allow a more accurate description of thermal food processing, especially when the safety of marginal heat processes are concerned.