Many physical properties of oxides can be changed by inducing lattice distortions in the crystal through heteroepitaxial growth of thin films. The average lattice strain can often be tuned by changing the film thickness or using suitable buffer layers between film and substrate. The exploitation of the full potential of strain engineering for sample or device fabrication rests on the understanding of the fundamental mechanisms of stress generation and evolution. For this study an optical measurement of the substrate curvature is used to monitor in situ how the stress builds up and relaxes during the growth of oxide thin films by pulsed laser deposition. The relaxation behavior is correlated with the growth mode, which is monitored simultaneously with reflection high-energy electron diffraction. The stress relaxation data is fitted and compared with theoretical models for stress evolution which were established for semiconductor epitaxy. The initial stage of the growth appears to be governed by surface stress and surface energy effects, while the subsequent stress relaxation is found to be fundamentally different between films grown on single-crystal substrates and on buffer layers. The first case can be rationalized with established theoretical models, but these models fail in the attempt to describe the growth on buffer layers. This is most probably due to the larger average density of crystalline defects in the buffer layers, which leads to a two-step stress relaxation mechanism, driven first by the nucleation and later by the migration of dislocation lines.