The objective of this work is to develop adaptive control schemes to establish asymptotic closed-loop stabilization for a class of uncertain time-delay systems with time-varying delays and nonlinear dynamical perturbations. The plant parameter uncertainties are assumed to be parametric and norm-bounded, and the norm of the nonlinear perturbation is assumed to be bounded by a weighted norm of the state. Two main problems are investigated. In the first problem, an adaptive control scheme is developed to guarantee asymptotic closed-loop stabilization when the weight of the state norm is assumed to be known. In the second problem, however, the weight of the state norm is assumed to be unknown. The stability results are demonstrated via a continuous stirred tank reactor (CSTR) system.