Lattice-mismatch-induced surface or film stress has significant influence on the morphology of heteroepitaxial films. This is demonstrated using Sb surfactant-mediated epitaxy of Ge on Si(111). The surfactant forces a two-dimensional growth of a continous Ge film instead of islanding. Two qualitatively different growth regimes are observed. Elastic relaxation: Prior to the generation of strain-relieving defects the Ge film grows pseudomorphically with the Si lattice constant and is under strong compressive stress. The Ge film relieves strain by forming a rough surface on a nm scale which allows partial elastic relaxation towards the Ge bulk lattice constant. The unfavorable increase of surface area is outbalanced by the large decrease of strain energy. The change of film stress and surface morphology is monitored in situ during deposition at elevated temperature with surface stress-induced optical deflection and high-resolution spot profile analysis low-energy electron diffraction. Plastic relaxation: After a critical thickness the generation of dislocations is initiated. The rough phase acts as a nucleation center for dislocations. On Si(111) those misfit dislocations are arranged in a threefold quasi periodic array at the interface that accommodate exactly the different lattice constants of Ge and Si.