This project aims at engineering of excitonic resonances in the nonlinear coefficients in ZnO based nanostructures. The strong Coulomb interaction in ZnO leads to high excitonic binding energies and small Bohr radii. Using molecular beam epitaxy, low-dimensional structures such as quantum wells and quantum wires are fabricated which allow to gain control on the excitonic spectrum. Laser spectroscopy is used for investigation of the nonlinear processes. An ab-initio theory describes the experimental results. The project paves the way towards tailoring of the excitonic contributions to the nonlinear coefficients on the nanoscale.