Flexible organic electronic devices are protected from degradation by encapsulation in multilayered films having very low water vapor and oxygen permeabilities. Barrier structures including up to four dyads of inorganic and polymeric alternating layers, deposited on a polyethylene terephthalate (PET) substrate are required to reduce the permeation of environmental gases. The inorganic layers were deposited by e-beam evaporation of silicon oxide (SiOx) and the polymeric layer was a wet-chemically applied, inorganic-organic hybrid layer (ORMOCER®). It was coated on top of the SiOx, creating a smooth surface for the deposition of the second SiOx layer. For the experimental determination of the water vapor transmission rates, we developed a modified ultra-low permeation measurement device based on a constant-flow carrier-gas-system to measure both the transient and stationary water vapor permeation through high-barrier films. The accumulation of permeated water vapor before its transport to the detector results in the measurement of very low water vapor transmission rates (WVTRs) down to 2 x 10-5 g m-2 d-1 at temperatures from 23°C to 80°C and relative humidities from 15% to 90%. The measured WVTRs agree with those measured using a commercially available device Aquatran from MOCON®. In addition, the solubility and diffusion coefficients of the polymeric layers as well as the solubility coefficients of the SiOx layers of the multilayered structures were experimentally determined by sorption measurements. It has been found out that the steady-state WVTR of the multilayered barrier films was dominated by the permeability of the SiO? layer, whereas the high solubility and the thickness of ORMOCER® layer enclosed by the SiO? layers were responsible for the increased lag-time. Numerical simulations of the time dependent permeation provide deep insight into the barrier performance of such structures, also described by the ideal laminate or geometric defect model. Furthermore, a quasi-steady-state approximation was derived, which provides an analytical expression of the time dependent permeation rate for such structures. This approximation suggests the required design for the multilayered barrier film structures according to the targeted lifetime of the flexible organic electronic devices.