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Abstract: The statistical distributions of cosmogenic nuclide measurements from moraine boulders contain previously unused information on moraine ages, and they help determine whether moraine degradation or inheritance is more important on individual moraines. Here, we present a method for extracting this information by fitting geomorphic process models to observed exposure ages from single moraines. We also apply this method to 94 10Be apparent exposure ages from 11 moraines reported in four published studies. Our models represent 10Be accumulation in boulders that are exhumed over time by slope processes (moraine degradation), and the delivery of boulders with preexisting 10Be inventories to moraines (inheritance). For now, we neglect boulder erosion and snow cover, which are likely second-order processes. Given a highly scattered data set, we establish which model yields the better fit to the data, and estimate the age of the moraine from the better model fit. The process represented by the better-fitting model is probably responsible for most of the scatter among the apparent ages. Our methods should help resolve controversies in exposure dating; we reexamine the conclusions from two published studies based on our model fits. [Copyright &y& Elsevier]