A model for simulating the dispersion processes of 137Cs and 239,240Pu in the Alborán Sea is described. The model consists of two hydrodynamic models: a 2D depth-averaged model and a two-layer model which provide tidal and geostrophic currents, respectively; a sediment transport model which provides suspended particle concentrations and sedimentation rates over the domain; and the radionuclide dispersion model including interactions of dissolved radionuclides with suspended particles and bed sediments. These processes are formulated using kinetic transfer coefficients. The hydrodynamic and sediment models are run and validated in advance, and their results are then used to simulate the dispersion of 137Cs and 239,240Pu, which are introduced from atmospheric fallout. Radionuclide concentrations in the water column and distributions in bed sediments have been compared with measurements in the sea. Both set of data are, in general, in agreement. The model has also been applied to calculate radionuclide fluxes through the Strait of Gibraltar. These computed fluxes have been compared with previous estimations as well.