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We investigate the long-distance salinity in a dual permeability coastal karst aquifer with a double conduit network using a three-dimensional variable-density groundwater flow and multispecies transport SEAWAT model. Sensitivity analyses were used to evaluate the impact of the parameters and boundary conditions on the modeling saltwater wedge in a karstic aquifer situated in the Cuban land territory, including hydraulic conductivity, vertical anisotropy and salinity concentration; both in the conduits network and the fractured medium. These analyses indicated that hydraulic conductivity of the fractured medium and salt concentration were the ones that have a stronger effect on saltwater intrusion in a karstic aquifer. We also show results of the three-dimensional numerical simulations on groundwater salinity for different scenarios with the variabilities of the important parameters and compare results with electric conductivity profiles measured in a well.