The theory of AC magnetoresistance in inhomogeneous solids is developed using the effective-medium theory. Calculations are performed for systems which consist of random high- and low-conductivity regions. The weak magnetic field H is directed along the z axis. The effective conductivity changes Delta sigma _m^xx and Delta sigma _m^zz and the magnetoresistance Delta rho _m^xx and Delta rho _m^zz in both the low- and the high-frequency regions are calculated up to the H² approximation. The calculations show that, owing to inhomogeneities, plateaux of the finite values Delta sigma _m^zz and Delta rho _m^zz in the low-frequency region occur. It is possible to have both Delta rho _m^xx> Delta rho _m^zz and Delta rho _m^xx< Delta rho _m^zz. In the high-frequency limit the equalities Delta sigma _m^zz= Delta rho _m^zz=0 hold as in homogeneous solids.