  Kramers-Kroenig (K-K) analysis of harmonic generation optical data is usually
greatly limited by the technical inability to measure data over a wide spectral
range. Data inversion for real and imaginary part of $\chi^{n}(n\omega; \omega,
>... ,\omega)$ can be more efficiently performed if the knowledge of one of the
two parts of the susceptibility in a finite spectral range is supplemented with
a single measurement of the other part for a given frequency. Then it is
possible to perform data inversion using only measured data and subtractive K-K
relations. In this paper multiply subtractive K-K relations are, for the first
time, presented for the nonlinear harmonic generation susceptibilities. The
applicability of the singly subtractive K-K relations are shown using data for
third-order harmonic generation susceptibility of polysilane.
