In　this　paper,　a　new　distributed　consensus　tracking　protocol　incorporating　local　disturbance　rejection　is　devised　for　a　multi-agent　system　with　heterogeneous　dynamic　uncertainties　and　disturbances　over　a　directed　graph.　It　is　of　two-degree-of-freedom　nature.　Specifically,　a　robust　distributed　controller　is　designed　for　consensus　tracking,　while　a　local　disturbance　estimator　is　designed　for　each　agent　without　requiring　the　input　channel　information　of　disturbances.　The　condition　for　asymptotic　disturbance　rejection　is　derived.　Moreover,　even　when　the　disturbance　model　is　not　exactly　known,　the　developed　method　also　provides　good　disturbance-rejection　performance.　Then,　a　robust　stabilization　condition　with　less　conservativeness　is　derived　for　the　whole　multi-agent　system.　Further,　a　design　algorithm　is　given.　Finally,　comparisons　with　the　conventional　one-degree-of-freedom-based　distributed　disturbance-rejection　method　for　mismatched　disturbances　and　the　distributed　extended-state　observer　for　matched　disturbances　validate　the　developed　method.　Manuscript　received　May　13,　2022;　accepted　June　12,　2022.　This　work　was　supported　by　the　National　Natural　Science　Foundation　of　China　(62003010,　61873006,　61673053),　the　Beijing　Postdoctoral　Research　Foundation　(Q6041001202001),　the　Postdoctoral　Research　Foundation　of　Chaoyang　District　(Q1041001202101),　and　the　National　Key　Research　and　Development　Project　(2018YFC1602704,　2018YFB1702704).　Recommended　by　Associate　Editor　Xiaohua　Ge.　　©　2014　Chinese　Association　of　Automation.