The compressive strain induced in epitaxial Sr4Fe6O13+/-delta (SFO) films of different thicknesses grown on SrTiO3 substrates is partially released by the modulation of the incommensurate oxygen superstructure along the a-axis parallel to the substrate [q=alpha a(m)* superspace group Xmmm(alpha 00)0s0]. The modulation alpha value varies proportionally to the in-plane a-parameter in a continuous range from 0.41, for fully strained thin films, of about 20-30 nm, to 0.44 for partially-relaxed thicker films of about 280 nm. This mechanism is responsible for the observed slow relaxation of the cell structure upon the film thickness increase in comparison with an equilibrium misfit dislocation-mediated relaxation. (C) 2005 American Institute of Physics.