A mixture of cereal flakes with dried fruit and with other additions is not a homogeneous material, thus, it is difficult to investigate it. During the production of such a mixture, its ingredients significantly differ by water activity, the product is not in the state of thermodynamic equilibrium, and the mass exchange occurs among those ingredients. The flakes, being a typical hygroscopic product, intensely absorb moisture, and the fruit is subject to desorption. Ingredients of the mixtures with the highest differences in water activity were selected for the investigation, i.e. cereal flakes (corn flakes and wheat bran flakes) and fruit (apple). Moisture sorption isotherms of those products were determined using a static exsiccation method. In the case of corn flakes and apples, the obtained isotherms represented type II according to the isotherm classification of Brunauer et al., and in the case of wheat bran flakes: type III of the same classification. Next, mixtures of flakes and apples were prepared; they had different water content levels. Slices of the fresh apples and of the apples dried so as to have 40, 60, and 80 % of dry matter were mixed with the flakes at a 1:10 constant ratio of dry matter. After a fixed time period, the mixtures were separated and the content of water & water activity were determined in the ingredients of those mixtures. The experiment was continued until the state of equilibrium was achieved, i.e. until the water activity levels of all the ingredients became equal. An effective water diffusion coefficient was determined for apples using the Crank method, and, as for the flakes, a D_ef/L² quotient was calculated because it was difficult to measure their sizes. The water diffusion coefficient of the apple as measured in the flakes & fresh apple mixture was 2.43·10^-11 m²/s while the water diffusion coefficient for the apple subject to drying was similar (3.23 – 3.08·10^-13 m²/s) regardless of the experiment conditions. As for the flakes, the lower the water content in the apple was the lower the D_ef/L² quotient value was. This means that the water diffusion speed in the fruit constitutes the major resistance to mass transfer within the entire system. Therefore, the D_ef/L² values as obtained under this experiment cannot be regarded to be a reliable measure of water diffusion coefficient for the flakes.