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The problem of concern is fault diagnosis for systems with delayed measurements when sensor and (or) actuator faults exists. The main contribution consists in proposing a delay-free transformation approach for measurement delays and in the design approach of a new optimal fault diagnoser. First, the authors regard the fault states as the sub-states of an augmented system, and a delay-free transformation is proposed to transform the system with a delayed measurement vector into a delay-free one. Then a sufficient condition for observability is proved for the transformed system. By using the duality principle, the design problem of the optimal fault diagnoser is transformed into an equivalent optimal control problem for the duality system of the fault diagnosis error equation. Finally, the real-time fault diagnosis is realised by constructing a new reduced-order optimal fault diagnoser. A simulation example is given to demonstrate the feasibility and validity of the proposed scheme.