Abstract Two-dimensional (2D) monolayer materials are interesting systems due to an existence of optically non-active dark excitonic states. In this work, we formulate a theoretical model of an excitonic Auger process which can occur together with the trap-assisted recombination in such 2D structures. The interactions of intravalley excitons (bright and spin-dark ones) and intervalley excitons (momentum-dark ones) with deep states located in the energy midgap have been taken into account. The explanation of this process is important for the understanding of excitonic and photoelectrical processes which can coexist in 2D materials, like transition metal dichalcogenides and perovskites.