We have grown compositionally graded Ge(x)Si1-x layers on Si at 900-degrees-C with both molecular beam epitaxy and rapid thermal chemical vapor deposition techniques. Triple-crystal x-ray diffraction reveals that for 0.10 < x < 0.53, the layers are totally relaxed. Ge(x)Si1-x, cap layers grown on these graded layers are threading-dislocation-free when examined with conventional plan-view and cross-sectional transmission electron microscopy. Electron beam induced current images were used to count the low threading dislocation densities, which were 4 X 10(5) +/- 5 X 10(4) cm-2 and 3 X 10(6) +/- 2 X 10(6) cm-2 Eq. 2 X 10(6) cm-2 for x = 0.23 and x = 0.50, respectively. Photoluminescence spectra from the cap layers are identical to photoluminescence from bulk Ge(x)Si1-x.