Abstract: The crystal structure and the microstructure of epitaxial Sr4Fe6O13+/-delta thin films grown on a single-crystal SrTiO3 substrate by PLD have been investigated. A combination of electron diffraction and high-resolution microscopy allows us to refine the structure and to identify an incommensurate modulation in the Sr4Fe6O13+/-delta films. The incommensurate structure (q = alphaa(m)* approximate to 0.39alpha(m)*, superspace group Xmmm(alpha00)0s0) can be interpreted as an oxygen-deficient modification in the Fe2O2.5 double layers. Moreover, it is shown that the experimentally determined a component of the modulation can be used consistently to estimate the local oxygen content in the Sr4Fe6O13+/-delta films. The compound composition can therefore be described as Sr4Fe6O12+2alpha and the value alpha = 0.39 corresponds to a Sr4Fe6O12.78 composition. The misfit stress along the Sr4Fe6O13+/-delta/SrTiO3 interface is accommodated via both elastic deformation and inelastic mechanisms (misfit dislocations and 90degrees rotation twins). The present results also suggest the existence of SrFeO3 perovskite in the Sr4Fe6O13+/-delta films.