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The Rwenzori Mountains in Africa represent an extremely uplifted basement fault block at the eastern edge of the western branch of the East African Rift system, a large-scale rift system controlled by extensional stresses. The rugged alpine topography reaches an altitude of up to 5109 m, and the highest parts are ice-covered. Glacial landforms and moraines proof repeated more extensive glaciations during the last glacial cycles. In order to elucidate magnitudes and the varying role of erosional processes in shaping the relief of the Rwenzori Mountains over the past 2 mill. years, we performed numerical simulations with the landscape evolution programme ULTIMA THULE. It is controlled by a climate driver with temperature as a master variable as well as changing precipitation and evapotranspiration over time. The morphological processes considered are fluvial erosion, hillslope diffusion, and glacial abrasion, and the latter controlled by the simulated glaciation of the landscape. We provide three sets of model runs: the first one starting from the present-day topography and running for approx. 800 ka, the second one extending the modelling period to 2 Ma, and the third one starting from a peneplain and evolving for 2 Ma. Our results provide constraints on the temperature history of the Rwenzori Mountains, the interplay of morphological degradation and tectonic uplift, and a time frame for the formation of the mountain chain from a peneplain to the present relief. The modelled landscape evolves from a peneplain 2 Ma ago to a Rwenzori-type mountain range, when the fairly strong average rock uplift of 1–2 mm year−1 is compensated by a strong fluvial erosion component. The rock uplift rate is needed to obtain elevations above the equilibrium line altitude around 500 ka BP and results in surface uplift over time. Around that time, a periodic ice cap appears in the models, and glacial abrasion then limits the height of the Rwenzori Mountains to its present elevation. © 2015, Springer-Verlag Berlin Heidelberg.