Multi-Context Systems (MCS) are a powerful framework to interlink heterogeneous knowledge bases under equilibrium semantics. Recent extensions of MCS to dynamic data settings either abstract from computing time, or abandon a dynamic equilibrium semantics. We thus present streaming MCS, which have a run-based semantics that accounts for asynchronous, distributed execution and supports obtaining equilibria for contexts in cyclic exchange (avoiding infinite loops); moreover, they equip MCS with native stream reasoning features. Ad-hoc query answering is NP-complete while prediction is PSpace-complete in relevant settings (but undecidable in general); tractability results for suitable restrictions.