This paper presents a recursive method to design state and output feedback controllers for MIMO, block-feedforward linear systems with delays in the inputs, outputs, and interconnections between the blocks. The resulting controller is of predictor-type, which means that it contains finite integrals over past state and input values. The method is a generalization of the well-known model reduction approach for systems with input delay. A recursive procedure replaces delay terms with non-delay ones step by step, from the top of the cascade structure down. Controller gains are computed for the proxy system without delays, while the construction guarantees the same closed loop poles for the delay system and the proxy one. The observer is designed by applying the duality argument and the separation principle is also shown to apply. (C) 2010 Elsevier Ltd. All rights reserved.