The critical thickness of the two-dimensional growth of Ge on relaxed SiGe/Si(001) buffer layers different in Ge content is studied in relation to the parameters of the layers. It is shown that the critical thickness of the two-dimensional growth of Ge on SiGe buffer layers depends on the lattice mismatch between the film and the substrate and, in addition, is heavily influenced by Ge segregation during SiGe-layer growth and by variations in the growth-surface roughness upon the deposition of strained (stretched) Si layers. It is found that the critical thickness of the two-dimensional growth of Ge directly onto SiGe buffer layers with a Ge content of x = 11–36% is smaller than that in the case of deposition onto a Si (001) substrate. The experimentally detected increase in the critical thickness of the two-dimensional growth of Ge with increasing thickness of the strained (stretched) Si layer predeposited onto the buffer layer is attributed to a decrease in the growth-surface roughness and in the amount of Ge located on the surface as a result of segregation.