We consider a problem of global asymptotic regulation of a chain of integrators that has unknown time-varying delays in both states and input by output feedback. The time-varying delays are only known to be bounded, and their bounds and time-varying rates are unknown. To solve the considered problem, we introduce a newly designed adaptive output feedback controller. For system analysis, we give a new transformation and techniques in order to deal with new phenomena associated with unknown time-varying delays in states. (C) 2015 Elsevier Ltd. All rights reserved.