An interesting consequence of string dualities is that they reveal situations where the geometry of a string background appears to be globally ill defined, a phenomenon usually referred to as nongeometry. On the other hand, string theory contains extended objects with nontrivial monodromy around them, often dubbed defect or exotic branes in codimension-2. We determine and examine the worldvolume actions and the couplings of certain such branes. In particular, based on specific chains of T- and S-dualities, we derive the Dirac-Born-Infeld and Wess-Zumino actions, which describe the dynamics of type IIB five-branes as well as their couplings to the appropriate gauge potentials associated to mixed symmetry tensors. Based on these actions we discuss how these branes act as sources of nongeometric fluxes. In one case this flux is what is usually termed Q flux, associated to a T-fold compactification, while in the S-dual case a type of nongeometry related to the Ramond-Ramond sector is encountered.