Cramer-Rao bounds are derived for a class of systems that can be described by Wiener and Hammerstein models, where the linear part consists of a finite-impulse-response filter and the static nonlinearity is a polynomial. The derivation of the formulae hinges on the assumptions that the input is a zero-mean stationary gaussian process with a power spectral density that is everywhere continuous, and that the additive measurement noise is also zero-mean gaussian. Computer simulations are presented that show a close agreement between the performance of the prediction error method and the calculated CRB’s.