The Strait of Gibraltar and the Alborán Sea are the only connection between the Atlantic Ocean and the Mediterranean Sea. Intense shipping activities occur in the area, including transport of waste radionuclides and transit of nuclear submarines. Thus, it is relevant to have a dispersion model that can be used in an emergency situation after an accident, to help the decision-making process. Such dispersion model requires an appropriate description of the physical oceanography of the region of interest, with simulations of tides and residual (average) circulation. In this work, a particle-tracking dispersion model that can be used to simulate the dispersion of radionuclides in the system Strait of Gibraltar-Alborán Sea is described. Tides are simulated using a barotropic model and for the average circulation a reduced-gravity model is applied. This model is able to reproduce the main features of the Alborán circulation (the well known Western Alborán Gyre, WAG, and the coastal circulation mode). The dispersion model is run off-line, using previously computed tidal and residual currents. The contamination patch is simulated by a number of particles whose individual paths are computed; diffusion and decay being modelled using a Monte Carlo method. Radionuclide concentrations may be obtained from the density of particles per water volume unit. Results from the hydrodynamic models have been compared with observations in the area. Several examples of dispersion computations under different wind and circulation conditions are presented.