The theory underlying a six-wave mixing experiment is developed using the methods of molecular quantum electrodynamics. This general theory allows the intensity of the second harmonic radiation generated by the six-wave process to be found for arbitrary arrangements of the generating laser beams. Several different polarization geometries are treated in detail, and comparison is made to experiments performed using near-resonant conditions. The agreement is good in all cases and allows detailed information pertaining to the six-wave tensor to be extracted. The information thus obtained provides evidence of a marked departure from Kleinman symmetry.