We have studied the strain relaxation inSi1−xGex/Si(001) structures with high electron mobility grown by molecular beam epitaxy. The structures contain aSi1−xGexlayer with linearly graded composition, followed subsequently by a uniform composition bufferSi1−yGey,a thin Si layer serving as two-dimensional electron gas channel, and a modulationn-dopedSi1−xGexlayer. We found that a major part of the graded layer is basically completely strain relaxed, whereas a very thin layer close to the graded-uniform layer interface, as well as the uniform alloy buffer, are just partly relaxed. We performed also model calculations of the strain status of a graded-uniform two-layer system using an equilibrium approach. It is found that for ourSi0.7Ge0.3systems, the residual strains of the samples with different composition, grading rate, and a uniform buffer thickness of 0.6 &mgr;m is almost the same at equilibrium. However, experiments show a clear dependence of the residual strain on the grading rate of the graded buffer. The higher the grading rate, the higher is the residual strain in the constant composition alloy buffer. This indicates that with a lower grading rate, the structure is closer to equilibrium, and is thus, thermally more stable. Furthermore, lower grading rates produce also smoother surfaces. ©1997 American Institute of Physics.