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A theoretical study is performed of the anomalous Hall effect in granular alloys with giant magnetoresistance. The calculation is carried out within the Kubo formalism and the Green’s function method. The mechanism of asymmetric scattering of the spin-polarized current carriers is considered with allowance for a size effect associated with scattering not only by one grain, but also with more complicated processes of transport among two and three grains. It is shown that scattering of conduction electrons by the interfaces of the grains and the matrix has a substantial effect on the magnitude of the anomalous Hall effect and determines its sign. In general, correlation between the quantities ρ _H and ρ ² is absent, where ρ _H is the Hall resistivity and ρ is the total resistivity of the granular alloy. However, numerical calculation shows that for certain values of the model parameters ρ _H∼ρ ^3.8 and for these same …