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Summary form only given. The organic salt 4-N,N-dimethylamino-4'-N'-methylstilbazolium toluene-p-sulfonate (DAST) is one of the best materials for second-order nonlinear optics. DAST crystals are very interesting especially for electro-optic applications because of their exceptionally large nonlinear optical susceptibilities and the good alignment of the chromophores in the crystal. Large-size crystals make DAST a promising material for such applications. Because of its large nonlinear optical susceptibilities, DAST is also a promising material for cascaded second-order nonlinearities where nonlinear phase shifts are induced by a combination of second-harmonic generation and difference-frequency generation or by the combination of optical rectification and the linear electro-optic effect. We show for the first time that the combination of optical rectification and the linear electro-optic effect leads to large effective third-order susceptibilities in pulsed degenerate four-wave mixing experiments in single crystals of DAST.