This　paper　investigates　the　consensusability　for　a　class　of　nonlinear　pure-feedback　multiagent　systems　(MASs)　with　delayed　full-state　constraints.　First,　by　using　a　novel　state-shifting　transformation　(SST),　the　constrained　states　are　encapsulated　into　some　barrier　functions　such　that　the　new　converted　state　variables　and　their　dynamic　model　are　generated.　Then,　the　essential　relationship　between　the　post-transformation　tracking　errors　and　the　pre-transformation　tracking　errors　are　further　explained.　By　employing　the　radial　basis　function　neural　networks　(RBF　NNs)　to　deal　with　the　unknown　nonlinearities　for　each　agent　and　introducing　a　relative　threshold　method　to　overcome　the　waste　problem　of　system　transmission　resources,　an　event-triggered　control　protocol　is　developed　for　the　considered　system.　The　proposed　protocol　has　its　own　advantages:　1)　This　is　the　first　work　to　consider　the　pure-feedback　MASs　with　delayed　full-state　constraints.　By　transforming　the　constrained　states　into　unconstrained　variables,　the　states　of　the　MASs　can　be　converged　into　ideal　ranges　within　a　predefined　time　$T$　;　2)　Under　this　control　protocol,　only　one　adaptive　law　is　necessary　to　be　updated　online　in　each　follower　and　the　use　efficiency　of　system　resources　is　improved　by　using　reasonable　event　triggering　mechanism.　Finally,　the　effectiveness　of　the　suggested　consensus　control　protocol　is　demonstrated　by　the　simulation　results.　Note　to　Practitioners-Delayed　constraints　often　encountered　in　practical　applications,　which　represent　a　type　of　constraints　that　may　be　violated　initially　but　required　to　be　satisfied　sometime　after　system　operation,　so　it　is　very　necessary　and　important　to　converge　states　into　ideal　ranges　within　a　predefined　time　when　delayed　constraints　required.　What＇s　more,　considering　the　requirement　of　high　control　accuracy　in　practical　application　and　the　current　Barrier　Lyapunov　Function　(BLF)　methods　need　to　restrict　the　virtual　control　signals　within　some　given　regions,　such　restrictive　conditions　make　the　design　and　implementation　of　the　traditional　controllers　particularly　difficult.　In　this　article,　the　control　protocol　for　a　class　of　nonlinear　pure-feedback　MASs　with　delayed　full-state　constraints　and　event-triggered　communication　are　constructed　to　promote　the　development　of　asymptotic　tracking　control　methods,　and　a　novel　state-shifting　transformation　is　used　to　ensure　the　system　states　could　be　converged　into　the　ideal　constrained　intervals　in　a　predefined　time.