We study the confinement of polysoaps in lyotropic smectic (L a ) and sponge (L 3 ) solutions of the nonionic surfactant pentaethylene glycol dodecyl ether (C 12 EO 5 ). The polysoap is a hydrophobically modified polymer with n-tetradecyl sidegroups randomly grafted to a polyacrylate backbone. Without the hydrophobic side chains the backbone polymer cannot be embedded into the intermembrane space, but confinement is achieved for a polysoap with as low as 1% of grafted groups. We measure by small angle x-ray and neutron scattering an increase of the bending rigidity of the lamellar membranes as a function of polysoap concentration. [S0031-9007(98)05642-7] PACS numbers: 83.70.Hq, 64.75. + g, 82.65.DpFluid membranes are two-dimensional structures, selfassembled from surfactant solutions [1]. In the biological realm, phospholipid bilayers constitute the walls of liposomes and cells, hosting proteins responsible for functions as diverse as anchoring the cytoskeleton, providing coating protection against the body immune response or opening ionic channels for osmotic compensation [2]. Membranes are also present in many surfactant based industrial formulations. For instance, the processing and delivery of detergents or conditioning agents often require at some stage the use of concentrated surfactant solutions where lyotropic liquid crystals are formed [3]. The simplest liquid crystalline phase of membranes is the lamellar phase L a , a smectic A lyotropic liquid crystal [4]. It consists of one-dimensional stacks of surfactant bilayers, separated by a solvent. Its one-dimensional symmetry allows for a relatively straightforward experimental determination of many properties pertaining not only to the ordered phase as a collective body of interacting membranes but also to each individual bilayer with its intrinsic constitutive elasticity [5]. Also of interest for our study is the sponge phase L 3 , a bicontinuous isotropic phase of multiconnected membranes [6]. The wealth of information collected over the past two decades on L a and L 3 phases designates them as convenient tools to investigate interactions between membranes and other components often present in synthetic or naturally occurring colloidal suspensions. L a phases have for instance been used to host ferromagnetic colloidal particles [7] and different types of polymers [8][9][10][11], both in the intermembrane solvent subphase [12,13] and inside the bilayer itself [14]. In this Letter we investigate by small angle x-ray and neutron scattering the structure of L a and L 3 phases with embedded polysoaps, a particular class of macromolecular surfactants. By studying a system of very flexible membranes, we were able to quantitatively determine, for the first time, the variation of the elastic constant of the membranes as a function of the concentration of added polymer.The L a and L 3 phases under investigation are composed of membranes of the nonionic surfactant C 12 EO 5 (from Nikko, Japan) and hexanol in a NaCl brine solution at 0.1M. Pure water͞C 12 EO 5 mixtur...