Constrained　by　production　capacity　and　the　pressure　to　reduce　emissions,　many　original　equipment　manufacturers　(OEMs)　authorize　third-party　remanufacturers　(TPRs)　to　remanufacture　patented　products.　We　investigate　the　operational　decisions　of　OEMs　and　authorized　TPRs　under　carbon　cap-and-trade　regulations　in　a　two-echelon　supply　chain.　We　first　formulate　an　operational　decision　model　for　OEMs　before　a　TPR　enters.　Then,　for　the　cases　of　centralized　and　decentralized　decision　making,　we　formulate　an　operational　decision-making　model　for　the　TPR　and,　subsequently,　establish　one　for　the　OEM　after　the　TPR　enters.　We　further　analyze　the　effects　of　carbon　emissions　cap,　trading　price　of　carbon　permits,　yield　rate,　and　consumer　willingness　to　pay　(WTP)　on　optimal　decisions.　Our　results　indicate:　whether　TPRs　accept　authorization　remanufacturing　depending　on　the　ratio　of　carbon　emissions　cap　to　carbon　emissions　for　producing　per　remanufactured　product;　royalty　rate　is　negatively　affected　by　trading　price　of　carbon　permits　and　per　remanufactured　product＇　carbon　emissions　other　than　that　for　per　new　product,　and　can　offset　the　threat　caused　by　TPRs;　the　implementation　of　carbon　cap-and-trade　regulations　causes　OEMs　to　charge　TPRs　lower　royalty　rate;　centralized　decision　making　increases　the　total　profit　of　the　supply　chain　and　delivers　superior　environmental　benefits.　As　yield　rate　and　WTP　increase,　the　total　profit　increases,　increasingly　sensitive　to　WTP.　©　2020　Biyu　Liu　et　al.