ZnSe1-xTex and BeyZn1-ySe1-xTex bulk crystals were grown using the traveling solvent method (TSM) with tellurium solution. Ternary bulk crystals of ZnSe1-xTex contained tellurium from 1.2 to 3.6 at% (0.025 < x < 0.072). Quaternary bulk crystals of BeyZn1-ySe1-xTex contained tellurium from 1.8 to 7.8 at% and beryllium from 0.02 to 6.9 at% (0.03 < x < 0.16, 0.0004 < y < 0.14). The tellurium effective segregation coefficient was obtained as k(Te) = 0.6 +/- 0.4 and the beryllium effective segregation coefficient was k(Be) = 1.7 +/- 0.5. In the ZnSeTe crystals, the best etch-pit density was 9.0 x 10(5)/cm(2) and the best full-width at half-maximum of the X-ray rocking curve was 50 arcscc. In the BeZnSeTe crystals, the best etch-pit density was 3.0 x 10(5)/cm(2) and the best full-width at half-maximum of the X-ray rocking curve was 33 arcsec. The Vickers hardness increased up to 4300 N/mm(2) in a beryllium concentration of 5 at%.