Deterioration of food products stored in flexible packaging materials can be attributed to the presence of both water and oxygen in the environment surrounding the food. Mathematical models for the simultaneous permeation of moisture and oxygen through the packaging polymeric film and subsequent adsorption on the food surface are presented for the case of competitive adsorption of the two diffusing species. These models are then used to predict internal packaging conditions over time for selected food products. Oxygen and moisture permeation are treated as independent phenomena, and the competition is regarded as occuring on a surface described by the Langmuir adsorption isotherm. It is found that for certain polymer physical properties and relative surface coverages, water and oxygen molecules can dislodge each other from the food surface and, even for situations where the initial partial pressure of oxygen is less than the external partial pressure, can cause an outward flow of the more weakly adsorbed material. This theory is then extended to incorporate varying external conditions of storage.