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In this paper we discuss the construction of non-geometric Q- and R-branes assources of non-geometric Q- and R-fluxes in string compactifications. Thenon-geometric Q-branes, being obtained via T-duality from the NS 5-brane orrespectively from the KK-monopole, are still local solutions of the standard NSaction, where however the background fields G and B possess non-geometricglobal monodromy properties. We show that using double field theory, redefinedbackground fields tilde G and beta as well as their corresponding effectiveaction, the Q-branes are locally and globally well behaved solutions.Furthermore the R-brane solution can be at least formally constructed usingdual coordinates. We derive the associated non-geometric Q- and R-fluxes anddiscuss that closed strings moving in the space transversal to theworld-volumes of the non-geometric branes see a non-commutative or anon-associative geometry.  In the second part of the paper we construct intersecting Q- and R-braneconfigurations as completely supersymmetric solutions of type IIA/Bsupergravity with certain SU(3) x SU(3) group structures. In the near horizonlimit the intersecting brane configurations lead to type II backgrounds of theform AdS4 x M6, where the six-dimensional compact space M6 is a torus fibrationwith various non-geometric Q- and R-fluxes in the compact directions. Itexhibits an interesting non-commutative and non-associate geometric structure.Furthermore we also determine some of the effective four-dimensionalsuperpotentials originating from the non-geometric fluxes.

Non-commutative/non-associative IIA (IIB) Q- and R-branes and their intersections