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The single and double phase macroscopic permeabilities of bimodal reconstructed porous media have been studied. The structure of these bimodal media is characterized by the micro and macroporosities (vug system) and by the micro and macrocorrelation lengths lp and lv. For a single phase, if the vugular system does not percolate, it is shown that the absolute permeability K mainly depends on lp and very little on the other parameters. However, when the vugs percolate, K is also influenced by the density of vugs. For double phase calculations (in strong wettability conditions), it is shown that a vuggy percolating system affects mainly the nonwetting phase permeability. Moreover, the relative permeabilities for a nonpercolating vuggy system are only slightly influenced by the porosity distribution. These predictions are in good agreement with some experimental data obtained with limestones.