Far-field continuous Global Positioning System (GPS) time-series data following the 2002 M7.9 Denali, Alaska earthquake imply that mantle viscoelastic rheology is stress-dependent. A linear viscous mantle cannot explain fast early displacement rates at the surface that rapidly decay with time, whereas a power-law rheology where strain rate is proportional to stress raised to the power of 3.5 ± 0.5 provides decay rates and spatial patterns in agreement with observations. This is consistent with laboratory measurements for hot, wet olivine, implying a hydrated mantle and a relatively thin (60-km-thick) lithosphere beneath south-central Alaska. These results suggest that the viscous strength of the lithosphere varies both spatially and temporally, and that effective viscosities inferred from different loading events or observational time-periods can differ by up to several orders of magnitude. Thus, the very conditions that enable the inference of rheologic strength–transient loading and unloading events–significantly alter the effective viscosity.