Relict rock glaciers are complex hydrogeological systems that might act as relevant groundwater storages; therefore, the discharge behavior of these alpine landforms needs to be better understood. Hydrogeological and geophysical investigations at a relict rock glacier in the Niedere Tauern Range (Austria) reveal a slow and fast flow component that appear to be related to the heterogeneous structure of the aquifer. A numerical groundwater flow model was used to indicate the influence of important internal structures such as layering, preferential flow paths and aquifer-base topography. Discharge dynamics can be reproduced reasonably by both introducing layers of strongly different hydraulic conductivities or by a network of highly conductive channels within a low-conductivity zone. Moreover, the topography of the aquifer base influences the discharge dynamics, which can be observed particularly in simply structured aquifers. Hydraulic conductivity differences of three orders of magnitude are required to account for the observed discharge behavior: a highly conductive layer and/or channel network controlling the fast and flashy spring responses to recharge events, as opposed to less conductive sediment accumulations sustaining the long-term base flow. The results show that the hydraulic behavior of this relict rock glacier and likely that of others can be adequately represented by two aquifer components. However, the attempt to characterize the two components by inverse modeling results in ambiguity of internal structures when solely discharge data are available.