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The influence of strain on diffusion and nucleation has been studied by means of scanning tunneling microscopy and effective-medium theory for Ag self-diffusion on strained and unstrained (111) surfaces. Experimentally, the diffusion barrier is observed to be substantially lower on a pseudomorphic Ag monolayer on Pt(111), 60 meV, compared to that on Ag(111), 97 meV. The calculations show that this strong effect is due to the 4.2% compressive strain of the Ag monolayer on Pt. It is shown that in general isotropic two-dimensional strain as well as its relief via dislocations have a drastic effect on surface diffusion and nucleation in heteroepitaxy and are thus of significance for the film morphology in the kinetic growth regime.