Structure and transport properties of ethylcellulose membranes with dispersed magnetic powder were investigated. The study mainly focused on diffusion, which is one of the transport mechanisms. The transport properties depend on many parameters like: polymeric matrix used, type of powder, its amount and granulation. The structure of the pattern formed by magnetic particles in the membrane matrix was studied. Description of the system was based on the phenomenological and molecular (random walk on a fractal lattice) approaches. Two parameters were calculated: the fractal dimension of random walk d_{w}, and the fractal dimension of membrane structure d_{f}. The knowledge of both parameters made it possible to use the generalized equation of diffusion on the fractal structure obtained by Metzler et al. The research was carried out to determine the influence of magnetic powder granulation on the transport properties. The results showed that the random walk within the membranes of the smallest magnetic powder granulation was of the most subdiffusive character. Detailed investigation and quantitative description of gas transport through the membranes enables designing the membranes to be used in air oxygen enrichment.