Summary: The asymptotic Cramér-Rao lower bound (CRLB) describes the best possible accuracy attainable by an efficient estimator as the number of data samples increase. It is developed here for the case of identifying noisy input-output systems. In this case, the measured variables and their statistical properties depend in a complicated way on the unknown parameters. A form of the CRLB is derived, generalizing a classical result by Whittle to include also a deterministic component in the data. The case where the undisturbed input is an ARMA process and the measurement noise on the input and output are white is treated in detail, and an explicit computational algorithm is developed.