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This contribution considers the determination of material parameters by using a combination of the Levenberg-Marquardt method with the multiscale finite element method. The former is a gradient method for the minimization of a function while the latter belongs to the group of homogenization methods and serves to solve direct problems related to the modeling of composite materials. The illustrative numerical examples are concerned with the investigation of the elastic parameters for two-phase materials. Emphasis is placed on the discussion of convergence and sensitivity with respect to the initial guess. © 2010 Civil-Comp Press.