This paper is focused on the problem of adaptively stabilizing a class of linear dynamical systems with time-varying delay, in which some parameters are unknown-but-bounded. It is established that when certain structural constraints are met, then a non-adaptive output-feedback stabilizing controller can be constructed to render the closed-loop system ’globally practically stable’. When the uncertainty set is unknown, an adaptive controller is then developed. The controller consists of two-terms : a growth term and a nonlinear output-driven term whereby the associated coefficients are easily designed within a very wide range.