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Binary Lennard-Jones fluids consisting of “solvent” and “surfactant” molecules are studied as simplified model systems for amphiphilic molecules in solution. Using Monte Carlo and molecular dynamics simulations, we observe the self-assembly of the surfactant molecules into bilayer membranes. These bilayers are fluid since the surfactants exhibit rapid lateral diffusion. We also measure the interfacial tension and the compressibility modulus of these bilayers. We show that they exhibit a tensionless state and characterize the corresponding stress profile. In this way, we bridge the gap between previous theoretical studies which were based (i) on discrete models with atomic resolution and (ii) on continuum models in which the bilayer membrane is treated as a smooth surface.