The problem of compensation of input delays for unstable linear systems was solved in the late 1970s. Systems with simultaneous input and state delay have remained a challenge, although exponential stabilization has been solved for systems that are not exponentially unstable, such as chains of delayed integrators and systems in the 'feedforward' form. We consider a general system in strict-feedback form with delayed integrators, which is an example of a particularly challenging class of exponentially unstable systems with simultaneous input and state delays, and design a predictor feedback controller for this class of systems. Exponential stability is proven with the aid of a Lyapunov-Krasovskii functional that we construct using the PDE backstepping approach. (C) 2010 Elsevier Ltd. All rights reserved.