A model for the activity of radionuclides in sediments has been set up based on the one-dimensional advection-diffusion equation. The model considers sedimentation, mixing, and compaction. Observed distributions of deposit-feeding organisms, and the nature of physical disturbances indicate that a gaussian diffusion coefficient may be appropriate. Two-layer models with constant and gaussian mixing, respectively, in the upper layer are compared with measured Pb 210 profiles for two cores from Green Bay, Lake Michigan, and it is found that the maximal diffusion coefficient D0 in the gaussian model is considerably greater than the constant D value, e.g., D0?4 versus D = 0.2 cm2/year, if compaction effects are neglected. The solution for the gauusian model is based on an approximate power series method. Compaction can be taken into account by using an exponential sedimentation rate or bulk sediment density. By comparing with measured data for a Lake Ontario core it is seen that compaction alone can give an appreciable flattening of the activity curves near the top layers.