This　paper　investigates　the　optimal　tracking　issue　for　continuous　-time　(CT)　nonlinear　asymmetric　constrained　zero　-sum　games　(ZSGs)　by　exploiting　the　neural　critic　technique.　Initially,　an　improved　algorithm　is　constructed　to　tackle　the　tracking　control　problem　of　nonlinear　CT　multiplayer　ZSGs.　Also,　we　give　a　novel　nonquadratic　function　to　settle　the　asymmetric　constraints.　One　thing　worth　noting　is　that　the　method　used　in　this　paper　to　solve　asymmetric　constraints　eliminates　the　strict　restriction　on　the　control　matrix　compared　to　the　previous　ones.　Further,　the　optimal　controls,　the　worst　disturbances,　and　the　tracking　Hamilton-Jacobi-Isaacs　equation　are　derived.　Next,　a　single　critic　neural　network　is　built　to　estimate　the　optimal　cost　function,　thus　obtaining　the　approximations　of　the　optimal　controls　and　the　worst　disturbances.　The　critic　network　weight　is　updated　by　the　normalized　steepest　descent　algorithm.　Additionally,　based　on　the　Lyapunov　method,　the　stability　of　the　tracking　error　and　the　weight　estimation　error　of　the　critic　network　is　analyzed.　In　the　end,　two　examples　are　offered　to　validate　the　theoretical　results.