An approach for modelling trophic transfer of persistent pollutants within aquatic food webs is described, using radioactivity as an example. This involves constructing a mass-balance trophic model of the ecosystem in question, applying the Ecopath software, which uses the biomass, production/biomass, and food consumption rates of the various functional groups in the ecosystem as its basic inputs, along with a diet matrix. The Ecopath outputs used in this study are the estimates of biomass flow between functional groups, and the corresponding predation mortality matrix, whose columns represent the intake of, and the rows the losses of biomass from a compartment. A set of first order differential equations, relating the intake and loss of biomass to the amounts of radioactivity in the compartments, are then set up. There is additional accounting for loss of radioactivity due to physical decay of the radioisotopes. The equations are integrated over time and calibrated by minimizing the sum of squared deviations between the observed and predicted levels of radioactivity, thus mapping the transfers of radioactivitiy onto the transfers of biomass. The method is demonstrated through (a) a case study of beta radioactivity in a coral reef ecosystem used as testing ground for nuclear weapons (Enewetak Atoll, Marshall Islands, Micronesia), and (b) preliminary data on '3'Cs in the upper trophic levels of the Central Baltic Sea ecosystem, following the 1986 Chernobyl accident. The results support the applicability of the approach, for which a general solution, involving an `importance-sampling' routine, is proposed.