The　main　challenge　for　analysing　system　time-dependent　performance　of　Compressed　Air　Energy　Storage　(CAES)　is　the　complexity　of　the　system　dynamic　characteristics　arisen　from　the　thermal,　mechanical,　chemical　and　electrical　sub-processes.　Identification　of　time-variant　interactions　between　these　sub-processes　is　essential　to　understand,　optimise　and　control　transient　behaviour　of　CAES　systems　in　practice.　Therefore,　this　study　proposed　a　new　detailed　cycle-to-cycle　modelling　framework　to　dynamically　simulate　an　adiabatic　CAES　(A-CAES)　system　with　packed　bed　Thermal　Energy　Storage　(PBTES).　The　detailed　cycle-to-cycle　modelling　framework　resolves　the　dynamics　of　associated　components,　links　the　time-variant　performance　of　the　components　in　each　cycle,　and　simulates　how　the　system　performs　from　the　start-up　to　the　steady-state　cycle　operation.　The　framework　provides　a　basis　for　further　time　dependent　analysis　and　control　of　both　the　components　and　the　system.　Using　the　model,　two　A-CAES　systems　using　packed　bed　thermal　stores,　one　filled　with　rock　and　the　other　one　filled　with　encapsulated　phase　change　material　(PCM),　were　analysed　and　compared.　The　time-resolved　simulation　indicated　a　higher　steady-state　cycle　efficiency　of　56.5%　for　the　system　with　the　PCM-filled　PBTES,　versus　53.2%　of　the　system　with　the　rock-filled　PBTES.　(C)　2017　The　Authors.　Published　by　Elsevier　Ltd.