It has been postulated that a steady state between erosional and tectonic processes may develop in continental collision. However, it is not clear whether steady state conditions can be reached for all components of the landscape. Here we show, using landscape evolution models and field evidence, that a true geomorphic steady state may never be reached in the Southern Alps of New Zealand. The strong asymmetries in tectonic uplift and tectonic advection and the onset of glaciations constantly interact to prevent the landscape from reaching a topographic steady state. Evidence suggests that the first-order geomorphology on the western side of the Southern Alps is controlled by orographic precipitation combined with extreme rates of tectonic uplift, whereas the development of deep glacial valleys on the eastern side is initiated by differential uplift along large faults. We also develop a first-order equation, governing the dynamics of the Main Divide, to show that both tectonic advection and fluvial erosion efficiency control the position and the height of the main drainage divide. Using a two-dimensional landscape evolution model, we demonstrate that the transition from glacial to fluvial conditions at the end of the last glaciation led to substantial modifications of the landscape: While the main trunk channels get slowly uplifted, ridges are leveled down, causing the relief to decrease. Hillslopes appear to be affected by fluvial processes which seem to be driven by incision of river tributaries. This reduction of relief will probably never reach a steady state since warmer interglacial periods are substantially shorter than glacial periods.