The permutation symmetry relations of the nth order nonlocal nonlinear optical susceptibilities emerging in the absence of absorption are obtained from the basic statements of electrodynamics. The values of the nth order nonlocal nonlinear susceptibility tensor components with swapped frequencies and indices corresponding to the generated electric field and the electric field under the operator of differentiation in the constitutive equation only differ by their signs and signs of the interchanged frequencies. Additionally, there exist n(2) - n relations between three components of this tensor with cyclically permuted indices and frequencies corresponding to the generated field, the field under the operator of differentiation in the constitutive equation and one of the remaining fields involved into nonlinear process under consideration.
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