We have investigated the properties of SiGe nanostructures fabricated by applying self-assembling and self-ordering processes during molecular beam epitaxy on vicinal Si surfaces without any lithographic patterning. Experimental parameters like growth temperature, orientation of the substrate surface versus (001) or (113), SiGe/Si multilayer buffer parameters, Ge content and Ge coverage have been varied systematically. The structures were analyzed by atomic force microscopy and transmission electron microscopy. During SiGe/Si multilayer deposition, surface steps on vicinal Si can develop to very regular, periodically arranged step bunches that serve as templates for the formation of SiGe wires. The spatial correlation of wires in different layers is either vertical or inclined, depending on sample surface, Ge content and multilayer period. Ge deposition on such a surface with periodical steps and strain domains results in nucleation of regular Ge wires, individual pearl strings of Ge islands, or two-dimensional close-packed arrays of Ge islands, depending on the buffer parameters. The experimental results demonstrate that different pathways of strain relaxation in SiGe nanostructures can be chosen by adequate growth parameters in order to control the nucleation of islands or wires, their lateral and vertical correlation, their size, and their shape. (C) 2000 Elsevier Science B.V. All rights reserved.