When a composite containing nonlinear dielectric particles suspended in a host medium is subjected to a sinusoidal alternating current (ac) electric field, the dielectric response of the composite will generally consist of ac fields at frequencies of higher order harmonics. For an electrorheological (ER) solid under structure transformations due to external fields, we apply the Ewald-Kornfeld formulation to derive the local electric fields and induced dipole moments explicitly, and then we perform the perturbation expansion method to extract their fundamental and third-order harmonics analytically. It is shown that the degree of anisotropy of the ER solid can affect these harmonics significantly. Our results are well understood in the spectral representation theory. Thus, it seems possible to perform a real-time monitoring of the structure transformation by measuring the nonlinear ac responses of ER solids.