We use the cosmic-ray-produced radionuclides 26Al and 10Be to date Plio-Pleistocene glacial sediment sequences. These two nuclides are produced in quartz at a fixed ratio, but have different decay constants. If a sample is exposed at the surface for a time and then buried by overburden and thus removed from the cosmic-ray flux, the 26Al/10Be ratio is related to the duration of burial. We first attempted to date pre-Wisconsinan tills by measuring 26Al and 10Be in fluvial sediments beneath them and applying the method of "burial dating," which previous authors have used to date river sediment carried into caves. This method, however, requires simplifying assumptions about the 26Al and 10Be concentrations in the sediment at the time of burial. We show that these assumptions are not valid for river sediment in glaciated regions. 26Al and 10Be analyses of such sediment do not provide accurate ages for these tills, although they do yield limiting ages in some cases. We overcome this difficulty by instead measuring 26Al and 10Be in quartz from paleosols that are buried by tills. We use a more general mathematical approach to determine the initial nuclide concentrations in the paleosol at the time it was buried, as well as the duration of burial. This technique provides a widely applicable improvement on other means of dating Plio-Pleistocene terrestrial glacial sediments, as well as a framework for applying cosmogenic-nuclide dating techniques in complicated stratigraphic settings. We apply it to pre-Wisconsinan glacial sediment sequences in southwest Minnesota and eastern South Dakota. Pre-Wisconsinan tills underlying the Minnesota River Valley were deposited 0.5 to 1.5 Ma, and tills beneath the Prairie Coteau in eastern South Dakota and adjacent Minnesota were deposited 1 to 2 Ma.