Accurate　traffic　congestion　prediction　is　crucial　for　efficient　urban　intelligent　transportation　systems　(ITS).　Though　most　existing　methods　attempt　to　characterize　spatial　correlation　and　temporal　correlation　in　traffic　congestion,　few　of　them　consider　spatial　heterogeneity　and　temporal　heterogeneity:　spatial　correlation　depends　on　temporality,　and　temporal　correlation　depends　on　spatiality　in　traffic　congestion.　To　address　this　problem,　this　paper　proposes　a　novel　approach　called　TCP-BAST　with　bilateral　alternation　to　simultaneously　capture　both　the　correlation　and　the　heterogeneity　between　spatiality　and　temporality　to　improve　traffic　congestion　prediction.　First,　to　capture　spatial　correlation　and　spatial　heterogeneity,　we　propose　a　spatial–temporal　alternation　(STA)　module　with　multi-head　graph　attention　networks　and　temporal　embedding.　Second,　to　capture　temporal　correlation　and　temporal　heterogeneity,　we　propose　a　temporal-spatial　alternation　(TSA)　module　with　multi-head　masked　attention　networks　and　spatial　embedding.　Third,　to　predict　the　traffic　congestion　of　multiple　road　sections　in　a　traffic　network,　we　propose　a　spatial–temporal　fusion　(STF)　module　to　fuse　the　multi-grained　spatial-temporal　features　derived　from　the　STA　and　TSA　modules.　The　experimental　results　on　a　real-world　traffic　dataset　demonstrate　that　the　proposed　TCP-BAST　approach　outperforms　the　baseline　methods　in　terms　of　both　the　mean　absolute　error　(MAE)　and　the　root　mean　squared　error　(RMSE).　Both　spatial-temporal　alternation　and　temporal-spatial　alternation　are　important　for　improving　traffic　congestion　prediction,　with　the　former　being　more　critical　than　the　latter.　©　2022　Elsevier　Inc.