It can easily be expected that debris-covered glaciers show a different response on external forcing compared to clean-surface glaciers. The supra-glacial debris cover acts as an additional transfer layer for the energy exchange between atmosphere and ice. The related glacier reaction is the integral of local effects, which changes strongly between enhanced melt for thin debris layers and considerably reduced melt for thicker debris. Therefore, a realistic feedback study can only be performed, if both the ice flow and the debris-influenced melt is treated with a high degree of detail. We couple a full Stokes representation of ice dynamics and the most complete description of energy transfer through the debris layer, in order to describe the long-term glacier reaction in the coupled system. With this setup, we can show that steady-state conditions are highly unlikely for glaciers, in case debris is not unloaded from the surface. For continuous and complete debris removal from the lowermost glacier tongue, however, a balance of the debris budget and the glacier conditions are possible. Depending on displacement and removal processes, our results demonstrate that debris-covered glaciers have an inherent tendency to switch to an oscillating state. Then, glacier mass balance and debris balance are out of phase, such that glacier advance periods end with the separation of the heavily debris-loaded lowermost glacier tongue, at time scales of decades to centuries. As these oscillations are inherent and happen without any variations in climatic forcing, it is difficult to interpret modern observations on the fluctuation of debris-covered glaciers on the basis of a changing climate only.