In this paper, an adaptive neural design is presented for a class of parametric-strict-feedback nonlinear systems with unknown time delays. The proposed design method does not require the a priori knowledge of the signs of the unknown virtual control coefficients. The unknown time delays are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. It is proved that the proposed backstepping design method is able to guarantee semi-global uniformly and ultimately boundedness of all the signals in the closed-loop.