Boulders and landscapes preserved beneath cold-based, non-erosive glacial ice violate assumptions associated with simple cosmogenic exposure dating. In such a setting, simple single isotope exposure ages over-estimate the latest period of surface exposure; hence, alternate approaches are required to constrain the multi-stage exposure/burial histories of such samples. Here, we report 28 paired analyses of 10Be and 26Al in boulder samples from Thule, northwest Greenland. We use numerical models of exposure and burial as well as Monte Carlo simulations to constrain glacial chronology and infer process in this Arctic region dominated by cold-based ice. We investigate three specific cases that can arise with paired nuclide data: (1)exposure ages that are coeval with deglaciation and 26Al/10Be ratios consistent with constant exposure; (2)exposure ages that pre-date deglaciation and 26Al/10Be ratios consistent with burial following initial exposure; and (3)exposure ages that pre-date deglaciation and 26Al/10Be ratios consistent with constant exposure. Most glacially-transported boulders in Thule have complex histories; some were exposed for tens of thousands of years and buried for at least hundreds of thousands of years, while others underwent only limited burial. These boulders were probably recycled through different generations of till over multiple glacial/interglacial cycles, likely experiencing partial or complete shielding during interglacial periods due to rotation or shallow burial by sediments. Our work demonstrates that the landscape in Thule, like many high-latitude landscapes, was shaped over long time durations and multiple glacial and interglacial periods throughout the Quaternary.