The aim of the present work is an analytical and numerical investigation of non-centrosymmetric matter in interaction with multichromatic photon fields. The work is structured as follows: Chapter 1 recapitulates the methods and models used in this work to describe higher harmonics in non-centrosymmetric matter, which reflects the current state of research. In Chapter 2, the Hamiltonian structure of non-centro-symmetrically bound electrons in the non-linear potential is explored, the results of which are important for understanding the following, especially for understanding the frequency-dependent amplitude. In chapters 3 to 6 different phenomena of the physics of condensed hard matter are analyzed. Each of these chapters can be read independently of the others and each begins with a detailed introduction to the respective problem. In Chapters 3 and 4, this is the question of the exact classical mechanism for the nonlinear electron response in the time and Fourier domain. New results for nonlinearly activated and detuned systems are presented. Until now little was known apart from the simplest model of this kind, in the linear approximation. In particular, the changes with increasing non-linearity for arbitrary orders of the harmonics and subharmonics are investigated. In the following chapter 5, new results for the macroscopic optical response tensors are obtained with these findings, whereby chapter 6 concludes the work with the consideration of the collective behavior of non-centrosymmetrically bound electrons in the "Simplified bond-hyperpolarizability model" (SBHM).