Cu2CdSnS4 and alpha/beta-Cu2ZnSiS4 meet several criteria for promising nonlinear optical materials for use in the infrared (IR) region. Both are air-stable, crystallize in noncentrosymmetric space groups, and possess high thermal stabilities. Cu2CdSnS4 and alpha/beta-Cu2ZnSiS4 display wide ranges of optical transparency, 1.4-25 and 0.7-25 mu m, respectively, and have relatively large second-order nonlinearity as well as phase matchability for wide regions in the IR. The laser-damage threshold (LDT) for Cu2CdSnS4 is 0.2 GW/cm(2), whereas alpha/beta-Cu2ZnSiS4 has a LDT of 2.0 GW/cm(2) for picosecond near-IR excitation. Both compounds also exhibit efficient third-order nonlinearity. Electronic structure calculations provide insight into the variation in properties.