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Many volcanoes emit a significant portion of the gas they transport to the atmosphere during continual passive degassing rather than during eruptions. To maintain a high gas and thermal flux without erupting magma, the flow field in the volcanic conduit must be approximately balanced with gas-rich, buoyant magma ascending and degassed, heavy magma descending. In vertical conduits, this exchange flow takes the form of core–annular flow, where the gas-rich magma forms a core enclosed by an annulus of degassed magma. The flow dynamics of core–annular flow have been studied extensively in fluid dynamics, but mostly for constant material properties. Our study aims to advance our understanding of how core–annular flow responds to volatile exsolution – a simple, yet ubiquitous disruption in volcanic conduits, which alters both the density and the viscosity of the core fluid. By deriving an evolution equation for the core–annular interface based on a generalized exchange-flow condition using a lubrication approximation, we find that the response of the system to volatile exsolution depends on the conduit flow regime. The same nucleation event can lead to a flow adjustment only in the upper, only in the lower or in both portions of the volcanic conduit. Our results emphasize that the thermodynamic evolution of magma properties and volcanic conduit flow are intricately linked, which may help understand the observed variability of eruptive behaviour at persistently degassing volcanoes.