  We present a consistent theoretical approach for calculating effective
nonlinear susceptibilities of metamaterials taking into account both frequency
and spatial dispersion. Employing the discrete dipole model, we demonstrate
that effects of spatial dispersion become especially pronounced in the vicinity
of effective permittivity resonance where nonlinear susceptibilities reach
their maxima. In that case spatial dispersion may enable simultaneous
generation of two harmonic signals with the same frequency and polarization but
different wave vectors. We also prove that the derived expressions for
nonlinear susceptibilities transform into the known form when spatial
dispersion effects are negligible. In addition to revealing new physical
phenomena, our results provide useful theoretical tools for analysing resonant
nonlinear metamaterials.
