FCT grant SFRH/BPD/100906/2014 and M. Knorr by FCT grant SFRH/BPD/86970/2012. German Research Foundation (DFG) grants BR-1817/7-1 and FOR 1513We address the problem of global inconsistency in reactive multi-context systems (rMCSs), a framework for reactive reasoning in the presence of heterogeneous knowledge sources that can deal with continuous input streams. Their semantics is given in terms of equilibria streams. The occurrence of inconsistencies, where rMCSs fail to have an equilibria stream, can render the entire system useless. We discuss various methods for handling this problem, following different strategies such as repairing the rMCS, or even relaxing the notion of equilibria stream so that it can go through inconsistent states.pr...