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The present publication provides a detailed theoretical approach to the elastic properties of one- and two-component amphiphilic membranes. It is formulated in terms of the molecular free energy aiming at an application to molecular models. The work focuses on the bending elastic moduli and the difference between the condition of constant surface tension and constant chemical potentials. It is found that the bending modulus of mean curvature becomes negative for two-component membranes approaching the limit of phase separation at constant chemical potentials. The treatment of bilayer membranes explicitly integrates monolayer-monolayer coupling. This is beneficial for the assessment of coupling effects for specific molecular models. The article is completed by a comprehensive continuum mechanical description of one-component monolayers. Based on the generalized Laplace equation it …