Recent observations indicate that many marine-terminating glaciers in Greenland and Antarctica are currently retreating and thinning, potentially due to long-term trends in climate forcing. In this study, we describe a simple two-stage model that accurately emulates the response to external forcing of marine-terminating glaciers simulated in a spatially extended model. The simplicity of the model permits derivation of analytical expressions describing the marine-terminating glacier response to forcing. We find that there are two time scales that characterize the stable glacier response to external forcing, a fast time scale of decades to centuries, and a slow time scale of millennia. These two time scales become unstable at different thresholds of bed slope, indicating that there are distinct slow and fast forms of the marine ice sheet instability. We derive simple expressions for the approximate magnitude and transient evolution of the stable glacier response to external forcing, which depend on the equilibrium glacier state and the strength of nonlinearity in forcing processes. The slow response rate of marine-terminating glaciers indicates that current changes at some glaciers are set to continue and accelerate in coming centuries in response to past climate forcing and that the current extent of change at these glaciers is likely a small fraction of the future committed change caused by past climate forcing. Finally, we find that changing the amplitude of natural fluctuations in some nonlinear forcing processes, such as ice shelf calving, changes the equilibrium glacier state.