Creep and shrinkage of the confined concrete changes the dynamic performance of concrete-filled steel tubular (CFST) arch bridges over time. However, less attention is paid to the seismic behaviour of CFST arches considering such long-term effects. The effects of long-term behaviour on the dynamic strength of CFST arch bridges are analysed and discussed in detail in this paper. A novel dynamic stability analysis method for structures subjected to any arbitrary excitations is proposed and validated. The time-dependent properties of concrete have been numerically implemented and also the difference in concrete pouring time at different arch positions is considered. An existing large-span CFST arch bridge is analysed as a case study adopting the proposed method. Moreover, the long-term performance evolution of CFST sections are discussed. It is found that the creep-induced stress within CFST sections has a great influence on the dynamic stability of arch bridges. The critical peak ground acceleration (PGA) at the 1000th day of the service life is suggested as the reference value for the limit state under earthquake excitations. The influence of travelling wave effect and concrete pouring sequence are also investigated. Finally, the post-seismic performance of the whole bridge is evaluated.