We consider a potential field in piecewise-nonhomogeneous media having a regular structure. The basic structure consists of a doubly-periodic system of groups of arbitrary heterogeneous anisotropic inclusions. The heterogeneous inclusions present in each of these groups possess the same-periodicity as the basic structure; they thus form a substructure. The problem of uniquely determining the field in this structure reduces to a determination of the solutions of a second order homogeneous elliptic equation in each of the component domains, the solutions being required to satisfy coupling conditions on the interfaces of the media and also some additional relationships. This boundary-value problem reduces to a system of regular integral equations, which we prove to be solvable. Questions arise in connection with the modelling of piecewise-nonhomogeneous anisotropic regular structures of a general type by means of homogeneous anisotropic media. As applications, we consider certain problems in hydromechanics and in the theory of anisotropic reinforced materials.