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Colletotrichumspecies are the most important postharvest spoilage fungi of papaya fruit. The objective of this research was to evaluate the effect of temperature and relative humidity on growth rate and time for growth to become visible of five strains of Colletotrichum gloeosporioidesisolated from papaya fruit in a complex medium. As a primary model, the radial growth rates were estimated using the Baranyi and Roberts model in papaya agar. The Solver MS Excel function was used to obtain the time to visible mycelium (tv). Secondary models obtained with the Rosso et al. cardinal model of inflection were applied to describe the effect of temperature on the growth rate (μ). The Arrhenius-Davey model was used to model tv. The obtained models seem to be satisfactory for describing both μ and tv. The relative humidity had an effect on μ and tvfor all tested C. gloeosporioidesisolates, but no model accurately described the behavior of the fungus. External validation of models was performed with papaya fruit. Growth models were developed with the same models used in vitro. The bias and the accuracy factors as indices for performance evaluation of predictive models in food microbiology as a function of temperature and RH were 1.22 and 1.33, respectively, for μ and 1.18 and 1.62, respectively, for tv,indicating accurate predictions. The supply chain of papaya is complex and requires constant conditions, and poor conditions can result in damage to the fruit. Knowledge of the behavior of C. gloeosporioideson papaya fruit and application of the developed models in the supply chain will help to establish transport control strategies to combat these fungi. This research has contributed to development of the first models of growth for C. gloeosporioidesin Mexico.