This paper is concerned with observer based output feedback control of linear systems with both (multiple) input and output delays. Our recently developed truncated predictor feedback (TPF) approach for state feedback stabilization of time-delay systems is generalized to the design of observers. By imposing some restrictions on the open-loop system, two classes of observer based output feedback controllers, one being finite dimensional and the other infinite dimensional, are constructed. It is further shown that, the infinite dimensional observer based output feedback controllers can be generalized to linear systems with both time-varying input and output delays. It is also shown that the separation principle holds for the infinite dimensional observer based output feedback controllers, but does not hold for the finite dimensional ones. Numerical examples are worked out to illustrate the effectiveness of the proposed approaches. (C) 2013 Elsevier Ltd. All rights reserved.