The influence of the surface microroughness on the critical thickness for the two-dimensional growth of strained SiGe structures on Si(001) and Ge(001) substrates is investigated. A decrease in the critical thickness for the two-dimensional growth of Ge films with increasing number of lattice periods or a decrease in the thickness of Si spacer layers is found for Ge/Si lattices grown on Si(001) substrates. This change is related to an increase in the surface roughness with the accumulation of elastic energy in compressed structures. A comparative study of the growth of SiGe structures on Si(001) and Ge(001) substrates shows that the critical thickness for the two-dimensional growth of tensile-strained layers is much larger than for compressed layers in a wide range of SiGe-layer compositions at an identical (in magnitude) lattice mismatch between the film and substrate.