Global fallout is the main source of anthropogenic radionuclides in the Mediterranean Sea. This work presents Cs-137, Pu239+240 and Am-241 concentrations in the water column in the southwest Alboran Sea, which was sampled in December 1999. A sediment core was taken at 800 m depth in the area (35 degrees 47' N, 04 degrees 48'W). Pb-210, Ra-226, Cs-137 and Pu239+240 specific activities were measured at multiple depths in the core for dating purposes. Cs-137 and Pu239+240 profiles did not show defined peaks that could be used as time markers, and they extended up to depths for which the Pb-210-based constant rate of supply (CRS) dating model provided inconsistent dates. These profiles can be useful to test dating models, understood as particular solutions of a general advection-diffusion problem, if the time series of radionuclide inputs into the sediment is provided. Thus, historical records of depth-averaged Cs-137 and Pu239+240 concentrations in water, and their corresponding fluxes into the sediment, were reconstructed. A simple water-column model was used for this purpose, involving atmospheric fallout, measured distribution coefficient (k(d)) values, and a first-estimate of sedimentation rates. A dating model of constant mixing with constant sedimentation rate was applied successfully to three independent records (unsupported Pb-210, Cs-137 and Pu239+240), and provided the objective determination of mixing parameters and mass sedimentation rate. These results provide some insight into the fate of atmospheric inputs to this marine environment and, particularly, into the contribution from the Chernobyl accident.