Internal or hidden variables are often introduced in formulations of problems governing the behavior of the fields in heterogeneous media. These hidden variables reflect the influence of the processes on the microstructural scale. The talk discusses internal variables that are naturally related to the structure of the composite material. The equations for the evolution of these variables are determined by the spectral measure in the Stieltjes analytic representation of the effective properties of the composite. The spectral measure contains all essential information about the geometry of the media on the microscale and links it through the internal variables to the behavior of the heterogeneous material on the macroscale.