In　this　work,　a　neural-networks　(NNs)-based　adaptive　asymptotic　tracking　control　scheme　is　presented　for　a　class　of　uncertain　nonstrict　feedback　nonlinear　systems　with　time-varying　full-state　constraints.　First,　we　construct　a　novel　exponentially　decaying　nonlinear　mapping　to　map　the　constrained　system　states　to　new　system　states　without　constraints.　Instead　of　the　traditional　barrier　Lyapunov　function　methods,　the　feasible　conditions　which　require　the　virtual　control　signals　satisfying　the　constraint　requirements　are　removed.　By　employing　the　Nussbaum　design　method　to　eliminate　the　effect　of　unknown　control　gains,　the　general　assumption　about　the　signs　of　the　unknown　control　gains　is　relaxed.　Then,　the　nonstrict　feedback　form　of　the　system　can　be　pulled　back　to　the　strict　feedback　form　through　the　basic　properties　of　radial　basis　function　NNs.　Simultaneously,　the　intermediate　control　signals　and　the　desired　controller　are　constructed　by　the　backstepping　process　and　the　Nussbaum　design　method.　The　designed　controller　can　ensure　that　all　signals　in　the　whole　closed-loop　system　are　bounded　without　the　violation　of　the　constraints　and　hold　the　asymptotic　tracking　performance.　In　the　end,　a　practical　example　about　a　brush　dc　motor　driving　a　one-link　robot　manipulator　is　given　to　illustrate　the　effectiveness　of　the　proposed　design　scheme.