This　paper　is　concerned　with　the　problem　of　adaptive　neural　control　for　a　class　of　uncertain　or　ill-defined　nonaffine　nonlinear　systems.　Using　a　self-organizing　radial　basis　function　neural　network　(RBFNN),　a　direct　self-constructing　neural　controller　(DSNC)　is　designed　so　that　unknown　nonlinearities　can　be　approximated　and　the　closed-loop　system　is　stable.　The　key　features　of　the　proposed　DSNC　design　scheme　can　be　summarized　as　follows.　First,　different　from　the　existing　results　in　literature,　a　self-organizing　RBFNN　with　adaptive　threshold　is　constructed　online　for　DSNC　to　improve　the　control　performance.　Second,　the　control　law　and　adaptive　law　for　the　weights　of　RBFNN　are　established　so　that　the　closed-loop　system　is　stable　in　the　term　of　Lyapunov　stability　theory.　Third,　the　tracking　error　is　guaranteed　to　uniformly　asymptotically　converge　to　zero　with　the　aid　of　an　additional　robustifying　control　term.　An　example　is　finally　given　to　demonstrate　the　design　procedure　and　the　performance　of　the　proposed　method.　Simulation　results　reveal　the　effectiveness　of　the　proposed　method.