In　this　paper,　an　adaptive　finite-time　bipartite　consensus　tracking　control　strategy　is　presented　for　a　class　of　heterogeneous　nonlinear　nonstrict-feedback　multi-agent　systems　(MASs)　with　output　constraints.　Firstly,　to　deal　with　the　time-varying　output　constraints　problem,　an　improved　tan-type　nonlinear　mapping　(NM)　function　is　presented　for　the　first　time.　And　based　on　the　improved　NM　function,　a　novel　tracking　error　is　constructed　to　design　controller　for　each　agent,　which　guarantees　the　bipartite　consensus　tracking　is　achieved　while　constraints　requirement　is　not　violated.　Then,　a　state　observer　is　designed　to　estimate　the　unmeasurable　states　of　each　agent.　Moreover,　in　the　case　of　unbalanced　directed　topological　graph,　a　partition　algorithm　(PA)　is　employed　to　implement　bipartite　consensus　tracking　control.　The　developed　distributed　adaptive　finite-time　control　strategy　ensures　that　all　the　signals　in　the　closed-loop　system　are　bounded　and　the　bipartite　consensus　tracking　control　is　achieved　in　finite　time.　Finally,　the　validity　of　the　designed　control　strategy　is　demonstrated　by　a　simulation　experiment.　Note　to　Practitioners-At　present,　nonlinear　MASs　are　widely　used　in　practice,　such　as　robots　formation　control,　vehicular　platoon　systems　control,　etc.　This　paper　investigated　the　adaptive　finite-time　bipartite　consensus　tracking　control　problem　for　a　class　of　heterogeneous　nonlinear　nonstrict-feedback　MASs　with　output　constraints.　In　the　scenarios　of　practical　application,　these　two　situations　are　common:　1)　The　communication　topology　graph　of　nonlinear　MASs　is　unbalanced.　2)　The　output　of　each　agent　is　constrained.　Therefore,　this　paper　presents　an　improved　tan-type　NM　method　to　deal　with　the　time-varying　output　constraints　problem,　and　a　partition　algorithm　is　employed　to　implement　bipartite　consensus　tracking　control　based　on　the　unbalanced　communication　topology　graph.　Meanwhile,　the　nonsingular　finite-time　control　strategy　effectively　improves　the　convergence　of　the　studied　nonlinear　MASs.　In　addition,　the　system　model　and　backstepping　technology　used　in　this　paper　are　general　and　practical.