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Passive margin stratigraphy contains time‐integrated records of landscapes that have long since vanished. Quantitatively reading the stratigraphic record using coupled landscape evolution and stratigraphic forward models (SFMs) is a promising approach to extracting information about landscape history. However, there is no consensus about the optimal form of simple SFMs because there has been a lack of direct tests against observed stratigraphy in well‐constrained test cases. Specifically, the extent to which SFM behaviour over geologic space and timescales should be governed by local (downslope sediment flux depends only on local slope) versus nonlocal (sediment flux depends on factors other than local slope, such as the history of slopes experienced along a transport pathway) processes is currently unclear. Here, we develop a nonlocal, nonlinear SFM that incorporates slope bypass and long‐distance sediment transport, both of which have been previously identified as important model components but not thoroughly tested. Our model collapses to the local, linear model under certain parameterizations such that best‐fit parameter values can indicate optimal model structure. Comparing 2‐D implementations of both models against seven detailed seismic sections from the Southeast Atlantic Margin, we invert the stratigraphic data for best‐fit model parameter values and demonstrate that best‐fit parameterizations are not compatible with the local, linear diffusion model. Fitting observed stratigraphy requires parameter values consistent with important contributions from slope bypass and long‐distance transport processes. The nonlocal, nonlinear model yields improved fits to the data regardless of whether the model is compared against only the modern bathymetric surface or the full set of seismic reflectors identified in the data. Results suggest that processes of sediment bypass and long‐distance transport are required to model realistic passive margin stratigraphy and are therefore important to consider when inverting the stratigraphic record to infer past perturbations to source regions. [ABSTRACT FROM AUTHOR]