  Using classical electrodynamics we determine the higher harmonic radiation by
a nonspherical metal cluster in form of a matrix formalism. Extending the
theory for the source of the higher harmonic radiation for spherical metal
clusters as introduced by \"Ostling et al. [Z. Phys. D {\bf 28}, 169 (1993)] we
calculate the sources for nonspherical particles. Employing these sources we
develop the nonlinear Mie theory and determine the radiated higher harmonic
fields generated by the cluster. Our theory is valid for arbitrary shape and
arbitrary complex refractive index for cluster sizes much smaller and
comparable to the wavelength of the incident light.
