The migration of the naturally derived antimicrobial (AM) agents, linalool, carvacrol, and thymol, from low-density polyethylene (LDPE) films containing ethylene vinyl acetate (EVA) copolymer into the food simulants, isooctane and various ethanol/water mixtures, was studied with a view towards examining the applicability of a first-order kinetic approach as well as a diffusion model approach for describing these systems. The results suggest that the proposed models adequately describe the release of AM agents. The combination of kinetic and diffusion analyses can provide additional information about the release process using the same data set. The analyses suggest that the release of linalool from LDPE/EVA depends on the EVA content in the formulation and that an optimum level of EVA is required to minimize the rate of release. A modification of the existing "idealized diffusion" model is proposed that enables the model to be applied to systems that demonstrate a departure from linearity when subjected to conventional analysis. The applicability of the idealized diffusion model was compared with the "simulant-limited" model and the results suggest that the former model is appropriate for describing most real systems when the simulant (or foodstuff) is favored in the partitioning of the AM agent between the film and the simulant.