In　this　paper,　an　event-triggered　neural　critic　learning　algorithm　is　investigated　to　address　constrained　nonzero-sum　game　problems　with　discrete-time　nonaffine　dynamics.　First,　in　order　to　ensure　the　saturation　independence　of　two　controllers　in　the　nonzero-sum　game　problem,　we　adopt　two　different　boundaries　to　constrain　them　respectively.　Then,　a　novel　triggering　condition　is　designed　to　reduce　the　update　times　of　the　controllers,　which　achieves　the　purpose　of　less　calculation.　It　is　emphasised　that　the　triggering　condition　is　established　based　on　the　iteration　of　the　time-triggered　mechanism.　Meanwhile,　we　prove　that　the　real　cost　function　possesses　a　predetermined　upper　bound,　which　realises　the　cost　guarantee　of　the　controlled　system.　In　addition,　we　prove　that　the　closed-loop　system　using　the　developed　algorithm　is　asymptotically　stable　and　that　the　system　state　and　the　sampling　state　are　uniformly　ultimately　bounded　during　the　process　of　training　neural　networks.　Finally,　two　simulation　examples　are　conducted　to　demonstrate　the　effectiveness　of　the　proposed　algorithm.