In　this　paper,　based　on　the　adaptive　critic　control　method,　an　improved　event-based　trajectory　tracking　mechanism　of　continuous-time　(CT)　nonlinear　multiplayer　zero-sum　games　(MZSGs)　is　established.　It　is　worthy　of　note　that　previous　papers　studying　the　trajectory　tracking　issue　of　nonlinear　CT　MZSGs　only　apply　to　the　case　where　the　reference　trajectory　eventually　converges　to　zero.　Consequently,　this　paper　develops　an　improved　mechanism　to　overcome　this　weakness.　Later,　an　event-triggered　framework　is　brought　in　to　reduce　the　amount　of　computation　and　improve　control　efficiency.　In　this　process,　an　innovative　triggering　condition　is　provided.　At　the　same　time,　the　infamous　Zeno　behavior　is　ruled　out　through　theoretical　analysis.　Furthermore,　the　event-based　near-optimal　controls　and　event-based　near-worst　disturbances　for　tracking　error　dynamics　are　gained　by　building　and　adjusting　a　single　critic　neural　network.　Immediately　after,　by　utilizing　the　Lyapunov　method,　the　uniform　ultimate　boundedness　stability　of　the　tracking　error　and　the　weight　estimation　error　is　ensured.　Lastly,　an　example　containing　two　case　studies　is　offered　to　validate　the　validity　of　the　established　mechanism.　Note　to　Practitioners-Complex　industrial　processes　often　involve　multiple　control　inputs　and　may　also　be　affected　by　multiple　disturbances　at　the　same　time,　which　can　be　referred　to　as　a　MZSG.　Since　many　industrial　processes　can　be　viewed　as　a　tracking　question　of　nonlinear　systems　and　the　event-triggered　mechanism　can　decrease　the　computational　cost,　the　tracking　problem　for　event-based　nonlinear　MZSGs　is　studied　in　this　paper,　which　is　significant　for　control　practitioners.　Moreover,　the　Hamilton-Jacobi-Isaacs　equation　is　often　difficult　to　solve　when　dealing　with　the　game　problem.　Hence,　an　adaptive　critic　technique　is　presented　to　acquire　the　near-optimal　controls　and　the　near-worst　disturbances,　which　replaces　the　traditional　actor-critic　framework　and　thus　simplifies　the　theoretical　analysis.　Note　that　this　paper　proposes　an　innovative　triggering　condition　to　relax　the　restriction　on　the　choice　of　disturbance　rejection　level.　Compared　to　previous　works　dealing　with　the　tracking　problem　of　nonlinear　MZSGs,　the　method　presented　in　this　paper　makes　the　choice　of　the　reference　trajectory　more　flexible　and　thus　enhances　the　applicability　in　general　industrial　processes.　Finally,　stability　analysis　and　simulation　results　are　given.　Note　that　for　different　practical　situations,　practitioners　can　adjust　the　related　parameters　to　achieve　the　tracking　control　of　MZSGs　and　minimize　the　computational　cost.