Abstract." Lamellar (L~) and hexagonal (Hi) mesophases, formed in mixtures of water and polyethylene oxide (PEO) oleylethers (average EO-numbers 5 (a), 8.5 (b) and 14 (c)) and pure hexaoxyethylene dodecylether (d), were investigated with small-an~e X-ray diffraction. Analysis of repeat spacings shows a deviation from linear one-and two-dimensional swelling of L~ and P/l, respectively, when a transition to a mesophase with a larger curvature of the interface is approached. With regard to L~, in this respect similar behaviour is observed for a pure surfactant (d) and a surfactant with an EO-length distribution (b). It is proposed that, through the formation of aggregates of limited extent, water filled pores in the mesophases arise. This is confirmed by analysis of the intensity ratio of diffraction maxima of first and second order in L~. Models for finite aggregates are introduced. These consist of (1) lamellae, infinite in one direction and with variable length L in a direction perpendicular to the first, with cylindrical edges and (2) cylinders with variable length L bounded by spherical caps. According to these models, under certain conditions, finite aggregates may be formed without an increase of the interfadal area per surfactant molecule. Applying the models to the regions where non-linear swelling is observed, reasonable values for L are found, which decrease progressively when the phase transition is approached.