In　recent　years,　real-time　hybrid　testing　(RTHT)　has　been　applied　for　the　dynamic　testing　of　high-speed　trains　running　on　bridges.　A　guarantee　of　stability　for　the　RTHT　system　is　essential　to　achieve　a　safe　and　reliable　result.　However,　the　inherent　time-varying　characteristics　of　the　vehicle-bridge　coupled　system　pose　challenges　to　RTHT　stability　prediction.　This　study　aims　to　develop　a　stability　prediction　method　specifically　tailored　for　time-varying　RTHT　system.　Firstly,　the　vehicle-bridge　coupled　RTHT　was　modelled　using　a　discrete　state–space　representation　with　a　comprehensive　consideration　of　the　time-varying　vehicle-bridge　interaction　and　the　dynamics　of　the　shaking　table.　Subsequently,　a　time-varying　stability　criterion　was　derived　from　the　periodic　time-varying　state　matrix,　forming　the　basis　for　a　relative　stability　prediction　method.　The　validity　of　the　proposed　method　was　confirmed　through　simulations　and　experiments　employing　a　single-axle　interaction　within　the　vehicle-bridge　coupled　RTHT　system.　The　coupled　system　consisted　of　a　quarter-car　model　and　simply　supported　beams　were　used　as　an　example　to　evaluate　the　stability　and　accuracy　of　the　time-varying　RTHT.　The　results　showed　that　the　stability　increased　with　increasing　vehicle　speed.　Reducing　the　pure　time　delay　of　the　shaking　table　improved　both　stability　and　accuracy.　Increasing　the　effective　frequency　of　the　shaking　table　improved　the　accuracy　but　may　reduce　the　stability　of　the　RTHT.　©　2024　Elsevier　Ltd