Sequential　Cross-Domain　Recommendation　(CDR)　has　been　popularly　studied　to　utilize　different　domain　knowledge　and　users＇　historical　behaviors　for　the　next-item　prediction.　In　this　paper,　we　focus　on　the　cross-domain　sequential　recommendation　problem.　This　commonly　exist　problem　is　rather　challenging　from　two　perspectives,　i.e.,　the　implicit　user　historical　rating　sequences　are　difficult　in　modeling　and　the　users/items　on　different　domains　are　mostly　non-overlapped.　Most　previous　sequential　CDR　approaches　cannot　solve　the　cross-domain　sequential　recommendation　problem　well,　since　(1)　they　cannot　sufficiently　depict　the　users＇　actual　preferences,　(2)　they　cannot　leverage　and　transfer　useful　knowledge　across　domains.　To　tackle　the　above　issues,　we　propose　joint　Internal　multi-interest　exploration　and　External　domain　alignment　for　cross　domain　Sequential　Recommendation　model　(IESRec).　IESRec　includes　two　main　modules,　i.e.,　internal　multi-interest　exploration　module　and　external　domain　alignment　module.　To　reflect　the　users＇　diverse　characteristics　with　multi-interests　evolution,　we　first　propose　internal　temporal　optimal　transport　method　in　the　internal　multi-interest　exploration　module.　We　further　propose　external　alignment　optimal　transport　method　in　the　external　domain　alignment　module　to　reduce　domain　discrepancy　for　the　item　embeddings.　Our　empirical　studies　on　Amazon　datasets　demonstrate　that　IESRec　significantly　outperforms　the　state-of-the-art　models.　©　2023　ACM.