Pseudomorphic Si and SiGe layers have been grown by molecular beam epitaxy (MBE) on extremely thin silicon-on-insulator (SOI) substrates with top Si layer widths down to about 10 nm. A low-temperature substrate cleaning procedure (T-s < 800 degrees C) is required in order to avoid Si cluster formation induced by holes and defects of the SOI substrates. The relaxation behavior of very thin SiGe on SOI layers is studied which is expected to take place by elastic strain relaxation of the structure concomitant with a gliding at the Si/SiO2 interface. Novel concepts described here are Ge diffusion into SOI layers during deposition at high temperatures and relaxation of SOI/SiGe structures with very thin layers. They promise fabrication of relaxed virtual SOI/SiGe substrates without any dislocations, Partial strain relaxation takes place by annealing SOI/Si0.7Ge0.3 structures at T-A = 750 degrees C. Si layers with tensile strain up to about 0.3% have been realized on top of such relaxed buffer structures. Optical and atomic force microscopy (AFM) reveal smooth surfaces without cross-hatch. Transmission electron microscopy (TEM) indicates a few stacking faults which seem to be related to defects of the underlying SIMOX substrate.