The sheer complexity of modern systems requires compositional approaches to variability modelling. To manage the variability of large systems’ architecture, feature models are widely used at design-time, with several operators defined to allow their composition. However, complex systems’ architectures may evolve at run-time by acquiring new features and functionalities while respecting new constraints. To address this challenge, this paper defines composition operators for component-based run-time variability models that not only encode these feature model composition operators, but also ensure safe run-time reconfiguration. To prove the correctness and compositionality properties, we propose a novel multi-step UP-bisimulation equivalence and use it to show that the component-based run-time variability models preserve the semantics of the composed feature models. In addition, reachability results permit safe reconfiguration.