We have investigated the influence of strain on the morphology in metal heteroepitaxy at temperatures where growth is dominated by kinetics. Whereas Ag(111) homoepitaxy is three dimensional below 400 K, the growth of Ag On Pt(111) proceeds two dimensionally up to a critical film thickness after which a transition to 3D growth is observed. This critical thickness increases from 1 ML at 130 K to 6-9 ML at 300 K. It is demonstrated that the 2D growth in the heteroepitaxial system is due to the particular growth kinetics induced by the compressive strain of the Ag films. The strained Ag layers are found to have substantially lower activation barriers for interlayer mass transport compared to strain free Ag(111). Further, strain and its relief in dislocations also lead to layer-dependent nucleation densities. Both these effects strongly promote layer-by-layer growth. The transition to 3D growth is triggered by the structural transition from strained Ag layers to a perfect Ag(111) termination. It is generally expected that compressive strain promotes 2D growth. (C) 1997 Elsevier Science B.V.