Fed-batch and perfusion cell culture processes used to produce therapeutic proteins can use microfilters for product harvest. In this study, new explicit mathematical models of sieving loss due to internal membrane fouling, external membrane fouling, or a combination of the two were generated. The models accounted for membrane and cake structures and hindered solute transport. Internal membrane fouling was assumed to occur due to the accumulation of foulant on either membrane pore walls (pore-retention model) or membrane fibers (fiber-retention model). External cake fouling was assumed to occur either by the growth of a single incompressible cake layer (cake-growth) or by the accumulation of a number of independent cake layers (cake-series). The pore-retention model was combined with either the cake-series or cake-growth models to obtain models that describe internal and external fouling occurring either simultaneously or sequentially. The models were tested using well-documented sieving decline data available in the literature. The sequential pore-retention followed by cake-growth model provided a good fit of sieving decline data during beer microfiltration. The cake-series and cake-growth models provided good fits of sieving decline data during the microfiltration of a perfusion cell culture. The new models provide insights into the mechanisms of fouling that result in the loss of product sieving. (C) 2017 American Institute of Chemical Engineers