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In this paper, we discuss a model describing the global behavior of the two-phase incompressible flow in fractured porous media. The fractured medium is regarded as a porous medium consisting of two superimposed continua, a connected fracture system, which is assumed to be thin of order
, where
being the relative fracture thickness, and an
-periodic system of disjoint matrix blocks. We derive the global behavior of the fractured medium by passing to the limit as
, taking into account that the permeability of the blocks is proportional to
, while the permeability of the fractures is of order one and obtain the corresponding global
-model, i.e. the homogenized model with the coefficients depending on the small parameter
. In the
-model, we linearize the cell problem in the matrix block and then by letting
, we obtain the macroscopic model which does not depend on
and
, and is fully homogenized in the sense that all the coefficients are calculated in terms of given data and do not depend on the additional coupling or cell problems.