BACKGROUND Non-linear models making it possible to predict agricultural pest outbreaks and optimise control tactics are of primary importance for integrated pest management. The development period for immature stages of the fennel aphid Hyadaphis foeniculi (Passerini) (Hemiptera: Aphididae) at constant temperatures was modelled in order to determine mathematical functions for simulating the aphid's development. Non-linear models were used to describe the relationship between temperature and development rates of H. foeniculi subjected to constant temperatures. RESULTS The models used were found to be good fits for estimating H. foeniculi development rates as a function of temperature, with the exception of the Davidson model. The development time of H. foeniculi nymphs ranged from 2.73 days (first instar) to 6.18 days (fourth instar) at 15 °C, from 2.57 days (first instar) to 4.52 days (fourth instar) at 20 °C and from 1.53 days (first instar) to 2.05 days (fourth instar) at 28 °C. CONCLUSION These models provide important tools for better elucidation of the relationship between temperature and development rates in H. foeniculi. The results could be used for predicting the occurrence of the various immature stages of H. foeniculi in the fennel crop in Brazil, making it possible to predict more accurately the best periods for implementing pest control.