This paper shows criteria for robust stability and stabilization of linear state-delayed systems with structured uncertainty. We consider the structured uncertainty composed of repeated scalar-block and full-block forms and a time-varying state delay. Delay-dependent methods for robust stability and stabilization are provided in terms of linear matrix inequalities. For linear systems with structured uncertainty and a time-varying state delay, the proposed methods give less conservative results than those obtained via the methods accounting for only norm-boundedness of the uncertainty.