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The Rwenzori Mountains in western Uganda form an active rift-transfer zone in the western branch of the East African Rift System. Here we quantify local stress fields in high resolution from field observations of fault structures to shed light on the complex, polyphase tectonics expected in transfer zones. We apply the multiple inverse method, which is optimized for heterogeneous fault-slip data, to the northern and central Rwenzori Mountains. Observations from the northern Rwenzori Mountains show larger heterogeneity than data from the central Rwenzori, including unexpected compressional features; thus the local stress field indicates polyphase transpressional tectonics. We suggest that transpression here is linked to rotational and translational movements of the neighboring Victoria block relative to the Rwenzori block that includes strong overprinting relationships. Stress inversions of data from the central Rwenzori Mountains indicate two distinct local stress fields. These results suggest that the Rwenzori block consists of smaller blocks. © 2015, Springer-Verlag Berlin Heidelberg.