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The homogenization theory, used for the study of differential equations with periodic coefficients, with a rapid variation, is used in the paper for the analysis of the creep phenomenon of composite materials, reinforced with fibers. Generally, a polymer composite having a matrix with a viscoelastic response manifests a creep behavior. A good knowledge of mechanical constants allows us to predict the time response under the action of a load, which is important in engineering. The homogenization method is used to determine the engineering constants for a composite reinforced with carbon fibers. The method is applied for the particular case of fiber-reinforced unidirectional composites to obtain the equations that finally offer the required values. The epoxy matrix Fibredux 6376C is reinforced with carbon fibers T800 and the thermoplastic specimens made by APC2 material is reinforced with carbon fibers of the type IM6. The experimental results give a good concordance with the theoretical predictions.