This report studies the dielectric properties of mixtures with components that can have an arbitrary permittivity dyadic. The anisotropic inclusions are assumed to be spherical. In the analysis, a quasistatic approach is used, and it leads to the general Maxwell Garnett formula. This is represented in many forms, and depending on the orientation distribution of the inclusions, the effective permittivity can be dyadic or scalar. Special emphasis is on the case of random orientation of the inclusions. The macroscopic permittivity depends on seven parameters of the mixture, six coming from the symmetric and antisymmetric parts of the inclusion permittivity dyadic, and one from the volume fraction. Numerical illustrations focus on the gyrotropy effects that are shown to lead to sharp maxima and minima in the polarizabilities and macroscopic permittivities.