In this paper, we consider the control problem of linear systems with state time-delays when the control signal is affected by a possibly time-varying delay. The problem is solved by a chain of predictors under the assumption that a stabilizing control exists for the case of no input delay. This solution is then extended to the case of partial information when only delayed output is available, Both the input and the output delays may have arbitrary bounds. With respect to previous approaches to the same problem appeared recently in the literature the method proposed here has a simpler structure and in particular it does not need the computation of distributed terms. As a by-product we show that it is possible to derive an observer for a system with state and output delays from an observer for the same system without output delays. (C) 2017 Elsevier Ltd. All rights reserved.