Extensive research activity has been devoted to self-assembly of very small coherent islands. However, while island formation is commonly described by a widely used S– K growth scheme, more complex mechanisms based on competitive effects of kinetics and thermodynamics take place during the epitaxy of Si 1− x Ge x on Si(0 0 1). The aim of this paper is to explain the formation and the evolution of Si 1− x Ge x islands on Si(0 0 1). The paper presents a comprehensive investigation of the different growth modes of Si 1− x Ge x films (with x varying from 0 to 1) on Si(0 0 1) and Si(1 1 1). The results are presented in the form of kinetic morphological growth diagrams of as-grown samples. Two and four growth regimes are distinguished on (1 1 1) and (0 0 1) respectively. These growth regimes correspond to different levels of relaxation. In particular the four regimes observed on Si(0 0 1) correspond to (i) no relaxation in regime I (2D layer), (ii) 15–20% relaxation in regime II (“huts” islands with (1 0 5) facets), (iii) 20% and 50% relaxation in regime III (in “huts” and “domes” respectively) and (iv) 50% and 80% relaxation in regime IV (“domes” with bimodal size distribution). Every growth regime characteristic of as-grown sample is also associated with a specific equilibrium steady state morphology which is obtained after long-term annealing of the as-grown samples. In the two first regimes (no or small strain relaxation) the equilibrium morphology of highly strained Si 1− x Ge x deposits corresponds to (1 0 5) faceted islands. We show that these islands are stabilised by the compressive stress. As soon as strain is released, (1 0 5) facets disappear at the expense of the (1 1 3) and (1 1 1) facets and first-order transition occurs between “huts” and “domes” islands.